diff --git a/packages/babel-parser/src/tokenizer/types.js b/packages/babel-parser/src/tokenizer/types.js
index 2301759f38..34fd891c92 100644
--- a/packages/babel-parser/src/tokenizer/types.js
+++ b/packages/babel-parser/src/tokenizer/types.js
@@ -144,9 +144,9 @@ export const types: { [name: string]: TokenType } = {
   bitwiseOR: createBinop("|", 3),
   bitwiseXOR: createBinop("^", 4),
   bitwiseAND: createBinop("&", 5),
-  equality: createBinop("==/!=", 6),
-  relational: createBinop("</>", 7),
-  bitShift: createBinop("<</>>", 8),
+  equality: createBinop("==/!=/===/!==", 6),
+  relational: createBinop("</>/<=/>=", 7),
+  bitShift: createBinop("<</>>/>>>", 8),
   plusMin: new TokenType("+/-", { beforeExpr, binop: 9, prefix, startsExpr }),
   modulo: createBinop("%", 10),
   star: createBinop("*", 10),
diff --git a/packages/babel-preset-typescript/test/fixtures/jsx-compat/ts-invalid/options.json b/packages/babel-preset-typescript/test/fixtures/jsx-compat/ts-invalid/options.json
index 345e1f87c9..4c0aa12465 100644
--- a/packages/babel-preset-typescript/test/fixtures/jsx-compat/ts-invalid/options.json
+++ b/packages/babel-preset-typescript/test/fixtures/jsx-compat/ts-invalid/options.json
@@ -1,4 +1,3 @@
 {
-  "presets": [["react", {}, "before"], "typescript", ["react", {}, "after"]],
-  "throws": "Unexpected token, expected \"</>\" (1:6)"
+  "throws": "Unexpected token, expected \"</>/<=/>=\" (1:6)"
 }