diff --git a/.README/README.md b/.README/README.md
index be062c4..ffe9a24 100644
--- a/.README/README.md
+++ b/.README/README.md
@@ -193,6 +193,7 @@ When `true`, only checks files with a [`@flow` annotation](http://flowtype.org/d
 {"gitdown": "include", "file": "./rules/require-variable-type.md"}
 {"gitdown": "include", "file": "./rules/semi.md"}
 {"gitdown": "include", "file": "./rules/sort-keys.md"}
+{"gitdown": "include", "file": "./rules/sort-type-union-intersection-members.md"}
 {"gitdown": "include", "file": "./rules/space-after-type-colon.md"}
 {"gitdown": "include", "file": "./rules/space-before-generic-bracket.md"}
 {"gitdown": "include", "file": "./rules/space-before-type-colon.md"}
diff --git a/.README/rules/sort-type-union-intersection-members.md b/.README/rules/sort-type-union-intersection-members.md
new file mode 100644
index 0000000..fc7ad10
--- /dev/null
+++ b/.README/rules/sort-type-union-intersection-members.md
@@ -0,0 +1,101 @@
+### `sort-type-union-intersection-members`
+
+_The `--fix` option on the command line automatically fixes problems reported by this rule._
+
+Enforces that members of a type union/intersection are sorted alphabetically.
+
+#### Options
+
+You can specify the sort order using `order`.
+
+* `"asc"` (default) - enforce ascending sort order.
+* `"desc"` - enforce descending sort order.
+
+```js
+{
+  "rules": {
+    "flowtype/sort-type-union-intersection-members": [
+      2,
+      {
+        "order": "asc"
+      }
+    ]
+  }
+}
+```
+
+You can disable checking intersection types using `checkIntersections`.
+
+* `true` (default) - enforce sort order of intersection members.
+* `false` - do not enforce sort order of intersection members.
+
+```js
+{
+  "rules": {
+    "flowtype/sort-type-union-intersection-members": [
+      2,
+      {
+        "checkIntersections": true
+      }
+    ]
+  }
+}
+```
+
+You can disable checking union types using `checkUnions`.
+
+* `true` (default) - enforce sort order of union members.
+* `false` - do not enforce sort order of union members.
+
+```js
+{
+  "rules": {
+    "flowtype/sort-type-union-intersection-members": [
+      2,
+      {
+        "checkUnions": true
+      }
+    ]
+  }
+}
+```
+
+You can specify the ordering of groups using `groupOrder`.
+
+Each member of the type is placed into a group, and then the rule sorts alphabetically within each group.
+The ordering of groups is determined by this option.
+
+* `keyword` - Keyword types (`any`, `string`, etc)
+* `named` - Named types (`A`, `A['prop']`, `B[]`, `Array<C>`)
+* `literal` - Literal types (`1`, `'b'`, `true`, etc)
+* `function` - Function types (`() => void`)
+* `object` - Object types (`{ a: string }`, `{ [key: string]: number }`)
+* `tuple` - Tuple types (`[A, B, C]`)
+* `intersection` - Intersection types (`A & B`)
+* `union` - Union types (`A | B`)
+* `nullish` - `null` and `undefined`
+
+```js
+{
+  "rules": {
+    "flowtype/sort-type-union-intersection-members": [
+      2,
+      {
+        "groupOrder": [
+          'keyword',
+          'named',
+          'literal',
+          'function',
+          'object',
+          'tuple',
+          'intersection',
+          'union',
+          'nullish',
+        ]
+      }
+    ]
+  }
+}
+```
+
+<!-- assertions sortTypeUnionIntersectionMembers -->
diff --git a/src/index.js b/src/index.js
index 66bc783..96b8b57 100644
--- a/src/index.js
+++ b/src/index.js
@@ -35,6 +35,7 @@ import requireValidFileAnnotation from './rules/requireValidFileAnnotation';
 import requireVariableType from './rules/requireVariableType';
 import semi from './rules/semi';
 import sortKeys from './rules/sortKeys';
+import sortTypeUnionIntersectionMembers from './rules/sortTypeUnionIntersectionMembers';
 import spaceAfterTypeColon from './rules/spaceAfterTypeColon';
 import spaceBeforeGenericBracket from './rules/spaceBeforeGenericBracket';
 import spaceBeforeTypeColon from './rules/spaceBeforeTypeColon';
@@ -84,6 +85,7 @@ const rules = {
   'require-variable-type': requireVariableType,
   semi,
   'sort-keys': sortKeys,
+  'sort-type-union-intersection-members': sortTypeUnionIntersectionMembers,
   'space-after-type-colon': spaceAfterTypeColon,
   'space-before-generic-bracket': spaceBeforeGenericBracket,
   'space-before-type-colon': spaceBeforeTypeColon,
@@ -133,6 +135,7 @@ export default {
     'require-variable-type': 0,
     semi: 0,
     'sort-keys': 0,
+    'sort-type-union-intersection-members': 0,
     'space-after-type-colon': 0,
     'space-before-generic-bracket': 0,
     'space-before-type-colon': 0,
diff --git a/src/rules/sortTypeUnionIntersectionMembers.js b/src/rules/sortTypeUnionIntersectionMembers.js
new file mode 100644
index 0000000..4d212d7
--- /dev/null
+++ b/src/rules/sortTypeUnionIntersectionMembers.js
@@ -0,0 +1,237 @@
+const groups = {
+  function: 'function',
+  intersection: 'intersection',
+  keyword: 'keyword',
+  literal: 'literal',
+  named: 'named',
+  nullish: 'nullish',
+  object: 'object',
+  tuple: 'tuple',
+  union: 'union',
+  unknown: 'unknown',
+};
+
+// eslint-disable-next-line complexity
+const getGroup = (node) => {
+  switch (node.type) {
+  case 'FunctionTypeAnnotation':
+    return groups.function;
+
+  case 'IntersectionTypeAnnotation':
+    return groups.intersection;
+
+  case 'AnyTypeAnnotation':
+  case 'BooleanTypeAnnotation':
+  case 'NumberTypeAnnotation':
+  case 'StringTypeAnnotation':
+  case 'SymbolTypeAnnotation':
+  case 'ThisTypeAnnotation':
+    return groups.keyword;
+
+  case 'NullLiteralTypeAnnotation':
+  case 'NullableTypeAnnotation':
+  case 'VoidTypeAnnotation':
+    return groups.nullish;
+
+  case 'BooleanLiteralTypeAnnotation':
+  case 'NumberLiteralTypeAnnotation':
+  case 'StringLiteralTypeAnnotation':
+    return groups.literal;
+
+  case 'ArrayTypeAnnotation':
+  case 'IndexedAccessType':
+  case 'GenericTypeAnnotation':
+  case 'OptionalIndexedAccessType':
+    return groups.named;
+
+  case 'ObjectTypeAnnotation':
+    return groups.object;
+
+  case 'TupleTypeAnnotation':
+    return groups.tuple;
+
+  case 'UnionTypeAnnotation':
+    return groups.union;
+  }
+
+  return groups.unknown;
+};
+
+const fallbackSort = (a, b) => {
+  if (a < b) {
+    return -1;
+  }
+  if (a > b) {
+    return 1;
+  }
+
+  return 0;
+};
+
+const sorters = {
+  asc: (collator, a, b) => {
+    return collator.compare(a, b) || fallbackSort(a, b);
+  },
+  desc: (collator, a, b) => {
+    return collator.compare(b, a) || fallbackSort(b, a);
+  },
+};
+
+const create = (context) => {
+  const sourceCode = context.getSourceCode();
+
+  const {
+    checkIntersections = true,
+    checkUnions = true,
+    groupOrder = [
+      groups.keyword,
+      groups.named,
+      groups.literal,
+      groups.function,
+      groups.object,
+      groups.tuple,
+      groups.intersection,
+      groups.union,
+      groups.nullish,
+    ],
+    order = 'asc',
+  } = context.options[1] || {};
+
+  const sort = sorters[order];
+
+  const collator = new Intl.Collator('en', {
+    numeric: true,
+    sensitivity: 'base',
+  });
+
+  const checkSorting = (node) => {
+    const sourceOrder = node.types.map((type) => {
+      const group = groupOrder?.indexOf(getGroup(type)) ?? -1;
+
+      return {
+        group: group === -1 ? Number.MAX_SAFE_INTEGER : group,
+        node: type,
+        text: sourceCode.getText(type),
+      };
+    });
+
+    const expectedOrder = [...sourceOrder].sort((a, b) => {
+      if (a.group !== b.group) {
+        return a.group - b.group;
+      }
+
+      return sort(collator, a.text, b.text);
+    });
+
+    const hasComments = node.types.some((type) => {
+      const count =
+        sourceCode.getCommentsBefore(type).length +
+        sourceCode.getCommentsAfter(type).length;
+
+      return count > 0;
+    });
+
+    let prev = null;
+
+    for (let i = 0; i < expectedOrder.length; i += 1) {
+      const type = node.type === 'UnionTypeAnnotation' ? 'union' : 'intersection';
+      const current = sourceOrder[i].text;
+      const last = prev;
+
+      // keep track of the last token
+      prev = current || last;
+
+      if (!last || !current) {
+        continue;
+      }
+
+      if (expectedOrder[i].node !== sourceOrder[i].node) {
+        const data = {
+          current,
+          last,
+          order,
+          type,
+        };
+
+        const fix = (fixer) => {
+          const sorted = expectedOrder
+            .map((t) => {
+              return t.text;
+            })
+            .join(
+              node.type === 'UnionTypeAnnotation' ? ' | ' : ' & ',
+            );
+
+          return fixer.replaceText(node, sorted);
+        };
+
+        context.report({
+          data,
+          messageId: 'notSorted',
+          node,
+
+          // don't autofix if any of the types have leading/trailing comments
+          // the logic for preserving them correctly is a pain - we may implement this later
+          ...hasComments ?
+            {
+              suggest: [
+                {
+                  fix,
+                  messageId: 'suggestFix',
+                },
+              ],
+            } :
+            {fix},
+        });
+      }
+    }
+  };
+
+  return {
+    IntersectionTypeAnnotation (node) {
+      if (checkIntersections === true) {
+        checkSorting(node);
+      }
+    },
+    UnionTypeAnnotation (node) {
+      if (checkUnions === true) {
+        checkSorting(node);
+      }
+    },
+  };
+};
+
+export default {
+  create,
+  meta: {
+    fixable: 'code',
+    messages: {
+      notSorted: 'Expected {{type}} members to be in {{order}}ending order. "{{current}}" should be before "{{last}}".',
+      suggestFix: 'Sort members of type (removes all comments).',
+    },
+    schema: [
+      {
+        properties: {
+          checkIntersections: {
+            type: 'boolean',
+          },
+          checkUnions: {
+            type: 'boolean',
+          },
+          groupOrder: {
+            items: {
+              enum: Object.keys(groups),
+              type: 'string',
+            },
+            type: 'array',
+          },
+          order: {
+            enum: ['asc', 'desc'],
+            type: 'string',
+          },
+        },
+        type: 'object',
+      },
+    ],
+  },
+};
diff --git a/tests/rules/assertions/sortTypeUnionIntersectionMembers.js b/tests/rules/assertions/sortTypeUnionIntersectionMembers.js
new file mode 100644
index 0000000..4a43fa9
--- /dev/null
+++ b/tests/rules/assertions/sortTypeUnionIntersectionMembers.js
@@ -0,0 +1,93 @@
+export default {
+  invalid: [
+    {
+      code: 'type T1 = B | A;',
+      errors: [{message: 'Expected union members to be in ascending order. "A" should be before "B".'}],
+      output: 'type T1 = A | B;',
+    },
+    {
+      code: 'type T2 = { b: string } & { a: string };',
+      errors: [{message: 'Expected intersection members to be in ascending order. "{ a: string }" should be before "{ b: string }".'}],
+      output: 'type T2 = { a: string } & { b: string };',
+    },
+    {
+      code: 'type T3 = [1, 2, 4] & [1, 2, 3];',
+      errors: [{message: 'Expected intersection members to be in ascending order. "[1, 2, 3]" should be before "[1, 2, 4]".'}],
+      output: 'type T3 = [1, 2, 3] & [1, 2, 4];',
+    },
+    {
+      code: `
+        type T4 =
+          | [1, 2, 4]
+          | [1, 2, 3]
+          | { b: string }
+          | { a: string }
+          | (() => void)
+          | (() => string)
+          | 'b'
+          | 'a'
+          | 'b'
+          | 'a'
+          | string[]
+          | number[]
+          | B
+          | A
+          | string
+          | any;
+      `,
+      errors: [
+        {message: 'Expected union members to be in ascending order. "[1, 2, 3]" should be before "[1, 2, 4]".'},
+        {message: 'Expected union members to be in ascending order. "{ b: string }" should be before "[1, 2, 3]".'},
+        {message: 'Expected union members to be in ascending order. "{ a: string }" should be before "{ b: string }".'},
+        {message: 'Expected union members to be in ascending order. "() => void" should be before "{ a: string }".'},
+        {message: 'Expected union members to be in ascending order. "() => string" should be before "() => void".'},
+        {message: 'Expected union members to be in ascending order. "\'b\'" should be before "() => string".'},
+        {message: 'Expected union members to be in ascending order. "\'a\'" should be before "\'b\'".'},
+        {message: 'Expected union members to be in ascending order. "\'b\'" should be before "\'a\'".'},
+        {message: 'Expected union members to be in ascending order. "\'a\'" should be before "\'b\'".'},
+        {message: 'Expected union members to be in ascending order. "string[]" should be before "\'a\'".'},
+        {message: 'Expected union members to be in ascending order. "number[]" should be before "string[]".'},
+        {message: 'Expected union members to be in ascending order. "B" should be before "number[]".'},
+        {message: 'Expected union members to be in ascending order. "A" should be before "B".'},
+        {message: 'Expected union members to be in ascending order. "string" should be before "A".'},
+        {message: 'Expected union members to be in ascending order. "any" should be before "string".'},
+      ],
+      output: `
+        type T4 =
+          any | string | A | B | number[] | string[] | 'a' | 'a' | 'b' | 'b' | () => string | () => void | { a: string } | { b: string } | [1, 2, 3] | [1, 2, 4];
+      `,
+    },
+  ],
+  valid: [
+    {
+      code: 'type T1 = A | B;',
+    },
+    {
+      code: 'type T2 = { a: string } & { b: string };',
+    },
+    {
+      code: 'type T3 = [1, 2, 3] & [1, 2, 4];',
+    },
+    {
+      code: `
+        type T4 =
+          | any
+          | string
+          | A
+          | B
+          | number[]
+          | string[]
+          | 'a'
+          | 'a'
+          | 'b'
+          | 'b'
+          | (() => string)
+          | (() => void)
+          | { a: string }
+          | { b: string }
+          | [1, 2, 3]
+          | [1, 2, 4];
+      `,
+    },
+  ],
+};
diff --git a/tests/rules/index.js b/tests/rules/index.js
index 619b6a0..069e54f 100644
--- a/tests/rules/index.js
+++ b/tests/rules/index.js
@@ -46,6 +46,7 @@ const reportingRules = [
   'require-variable-type',
   'semi',
   'sort-keys',
+  'sort-type-union-intersection-members',
   'space-after-type-colon',
   'space-before-generic-bracket',
   'space-before-type-colon',