diff --git a/src/rules/newline-after-import.js b/src/rules/newline-after-import.js
index b6af0b9528..17a2657dcf 100644
--- a/src/rules/newline-after-import.js
+++ b/src/rules/newline-after-import.js
@@ -120,9 +120,8 @@ after ${type} statement not followed by another ${type}.`,
         const nodePosition = parent.body.indexOf(node)
         const nextNode = parent.body[nodePosition + 1]
         
-        // skip object imports
-        if (node.type === 'TSImportEqualsDeclaration' &&
-          (!node.moduleReference || node.moduleReference.type !== 'TSExternalModuleReference')) {
+        // skip "export import"s
+        if (node.type === 'TSImportEqualsDeclaration' && node.isExport) {
           return
         }
 
diff --git a/src/rules/order.js b/src/rules/order.js
index 7f0160fe10..15b266ca9b 100644
--- a/src/rules/order.js
+++ b/src/rules/order.js
@@ -615,6 +615,10 @@ module.exports = {
       TSImportEqualsDeclaration: function handleImports(node) {
         let name
         let type
+        // skip "export import"s
+        if (node.isExport) {
+          return
+        }
         if (node.moduleReference.type === 'TSExternalModuleReference') {
           name = node.moduleReference.expression.value
           type = 'import'