diff --git a/package.json b/package.json
index 0a3be799398..c9d37461356 100644
--- a/package.json
+++ b/package.json
@@ -19,7 +19,7 @@
     "compile:lockfile": "node tasks/compile-lockfile.js"
   },
   "devDependencies": {
-    "eslint": "6.1.0",
+    "eslint": "^6.1.0",
     "execa": "1.0.0",
     "fs-extra": "^7.0.1",
     "get-port": "^4.2.0",
diff --git a/packages/babel-preset-react-app/package.json b/packages/babel-preset-react-app/package.json
index e9f6d29dcbf..09b2e6aabf7 100644
--- a/packages/babel-preset-react-app/package.json
+++ b/packages/babel-preset-react-app/package.json
@@ -21,19 +21,19 @@
     "test.js"
   ],
   "dependencies": {
-    "@babel/core": "7.5.5",
+    "@babel/core": "7.6.0",
     "@babel/plugin-proposal-class-properties": "7.5.5",
-    "@babel/plugin-proposal-decorators": "7.4.4",
+    "@babel/plugin-proposal-decorators": "7.6.0",
     "@babel/plugin-proposal-object-rest-spread": "7.5.5",
     "@babel/plugin-syntax-dynamic-import": "7.2.0",
-    "@babel/plugin-transform-destructuring": "7.5.0",
+    "@babel/plugin-transform-destructuring": "7.6.0",
     "@babel/plugin-transform-flow-strip-types": "7.4.4",
     "@babel/plugin-transform-react-display-name": "7.2.0",
-    "@babel/plugin-transform-runtime": "7.5.5",
-    "@babel/preset-env": "7.5.5",
+    "@babel/plugin-transform-runtime": "7.6.0",
+    "@babel/preset-env": "7.6.0",
     "@babel/preset-react": "7.0.0",
-    "@babel/preset-typescript": "7.3.3",
-    "@babel/runtime": "7.5.5",
+    "@babel/preset-typescript": "7.6.0",
+    "@babel/runtime": "7.6.0",
     "babel-plugin-dynamic-import-node": "2.3.0",
     "babel-plugin-macros": "2.6.1",
     "babel-plugin-transform-react-remove-prop-types": "0.4.24"
diff --git a/packages/react-error-overlay/flow/env.js b/packages/react-error-overlay/flow/env.js
index 12b151f5e4b..d4d10e2806a 100644
--- a/packages/react-error-overlay/flow/env.js
+++ b/packages/react-error-overlay/flow/env.js
@@ -2,7 +2,7 @@ declare module 'anser' {
   declare module.exports: any;
 }
 
-declare module 'babel-code-frame' {
+declare module '@babel/code-frame' {
   declare module.exports: any;
 }
 
diff --git a/packages/react-error-overlay/package.json b/packages/react-error-overlay/package.json
index aa28f9dba96..92bf4d59337 100644
--- a/packages/react-error-overlay/package.json
+++ b/packages/react-error-overlay/package.json
@@ -35,9 +35,9 @@
   ],
   "devDependencies": {
     "@babel/code-frame": "7.5.5",
-    "@babel/core": "7.5.5",
+    "@babel/core": "7.6.0",
     "anser": "1.4.8",
-    "babel-eslint": "10.0.2",
+    "babel-eslint": "10.0.3",
     "babel-jest": "^24.8.0",
     "babel-loader": "8.0.6",
     "babel-preset-react-app": "^9.0.1",
diff --git a/packages/react-error-overlay/src/index.js b/packages/react-error-overlay/src/index.js
index e8fbbb0dfad..55e59aeaf5d 100644
--- a/packages/react-error-overlay/src/index.js
+++ b/packages/react-error-overlay/src/index.js
@@ -5,7 +5,6 @@
  * LICENSE file in the root directory of this source tree.
  */
 
-/* @flow */
 import {
   listenToRuntimeErrors,
   crashWithFrames,
diff --git a/packages/react-error-overlay/src/listenToRuntimeErrors.js b/packages/react-error-overlay/src/listenToRuntimeErrors.js
index 670dbb0f8e4..049a79e384a 100644
--- a/packages/react-error-overlay/src/listenToRuntimeErrors.js
+++ b/packages/react-error-overlay/src/listenToRuntimeErrors.js
@@ -5,7 +5,6 @@
  * LICENSE file in the root directory of this source tree.
  */
 
-/* @flow */
 import {
   register as registerError,
   unregister as unregisterError,
diff --git a/packages/react-scripts/package.json b/packages/react-scripts/package.json
index 6d86a6d8daa..b4740dc31bb 100644
--- a/packages/react-scripts/package.json
+++ b/packages/react-scripts/package.json
@@ -28,11 +28,11 @@
   },
   "types": "./lib/react-app.d.ts",
   "dependencies": {
-    "@babel/core": "7.5.5",
+    "@babel/core": "7.6.0",
     "@svgr/webpack": "4.3.2",
     "@typescript-eslint/eslint-plugin": "1.13.0",
     "@typescript-eslint/parser": "1.13.0",
-    "babel-eslint": "10.0.2",
+    "babel-eslint": "10.0.3",
     "babel-jest": "^24.8.0",
     "babel-loader": "8.0.6",
     "babel-plugin-named-asset-import": "^0.3.3",
diff --git a/tasks/e2e-simple.sh b/tasks/e2e-simple.sh
index ff6d2954b5f..de126e14633 100755
--- a/tasks/e2e-simple.sh
+++ b/tasks/e2e-simple.sh
@@ -94,12 +94,12 @@ startLocalRegistry "$root_path"/tasks/verdaccio.yaml
 ./node_modules/.bin/eslint --max-warnings 0 packages/eslint-config-react-app/
 ./node_modules/.bin/eslint --max-warnings 0 packages/react-dev-utils/
 ./node_modules/.bin/eslint --max-warnings 0 packages/react-scripts/
+./node_modules/.bin/eslint --max-warnings 0 packages/react-error-overlay/src/
 
 cd packages/react-error-overlay/
-./node_modules/.bin/eslint --max-warnings 0 src/
 yarn test
-if [ $APPVEYOR != 'True' ]; then
-  # Flow started hanging on AppVeyor after we moved to Yarn Workspaces :-(
+if [ $AGENT_OS != 'Windows_NT' ]; then
+  # Flow started hanging on Windows build agents
   yarn flow
 fi
 cd ../..