diff --git a/packages/babel-core/test/fixtures/transformation/misc/regression-2765/actual.js b/packages/babel-core/test/fixtures/transformation/misc/regression-2765/actual.js
new file mode 100644
index 0000000000..32f7a0ea52
--- /dev/null
+++ b/packages/babel-core/test/fixtures/transformation/misc/regression-2765/actual.js
@@ -0,0 +1,5 @@
+function f() {
+  let g = async () => {
+    this;
+  };
+};
diff --git a/packages/babel-core/test/fixtures/transformation/misc/regression-2765/expected.js b/packages/babel-core/test/fixtures/transformation/misc/regression-2765/expected.js
new file mode 100644
index 0000000000..edb9007102
--- /dev/null
+++ b/packages/babel-core/test/fixtures/transformation/misc/regression-2765/expected.js
@@ -0,0 +1,12 @@
+function f() {
+  var _this = this;
+
+  let g = function () {
+    var ref = babelHelpers.asyncToGenerator(function* () {
+      _this;
+    });
+    return function g() {
+      return ref.apply(this, arguments);
+    };
+  }();
+};
diff --git a/packages/babel-core/test/fixtures/transformation/misc/regression-2765/options.json b/packages/babel-core/test/fixtures/transformation/misc/regression-2765/options.json
new file mode 100644
index 0000000000..a6cc8b11cb
--- /dev/null
+++ b/packages/babel-core/test/fixtures/transformation/misc/regression-2765/options.json
@@ -0,0 +1,8 @@
+{
+  "plugins": [
+    "transform-es2015-arrow-functions",
+    "syntax-async-functions",
+    "transform-async-to-generator",
+    "external-helpers"
+  ]
+}
diff --git a/packages/babel-core/test/fixtures/transformation/misc/regression-7064/exec.js b/packages/babel-core/test/fixtures/transformation/misc/regression-7064/exec.js
new file mode 100644
index 0000000000..9b94389c6b
--- /dev/null
+++ b/packages/babel-core/test/fixtures/transformation/misc/regression-7064/exec.js
@@ -0,0 +1,23 @@
+class Bar {
+  test() {
+    // pass
+    (() => {
+      assert.strictEqual(this.constructor, Bar);
+    })();
+
+    // pass
+    (() => {
+      assert.strictEqual(this.constructor, Bar);
+    }).call(this);
+
+    (async () => {
+      assert.strictEqual(this.constructor, Bar);
+    })();
+
+    (async () => {
+      assert.strictEqual(this.constructor, Bar);
+    }).call(this);
+  }
+}
+
+(new Bar()).test();
diff --git a/packages/babel-core/test/fixtures/transformation/misc/regression-7064/options.json b/packages/babel-core/test/fixtures/transformation/misc/regression-7064/options.json
new file mode 100644
index 0000000000..5df260afd8
--- /dev/null
+++ b/packages/babel-core/test/fixtures/transformation/misc/regression-7064/options.json
@@ -0,0 +1,4 @@
+{
+  "plugins": ["transform-async-to-generator"],
+  "presets": ["es2015"]
+}