diff --git a/lib/6to5/transformation/modules/amd.js b/lib/6to5/transformation/modules/amd.js
index 56387fafb4..bfa4bfcf7c 100644
--- a/lib/6to5/transformation/modules/amd.js
+++ b/lib/6to5/transformation/modules/amd.js
@@ -31,12 +31,15 @@ AMDFormatter.prototype.transform = function (ast) {
 
   // build an array of module names
 
-  var names = [t.literal("exports")].concat(this.buildDependencyLiterals());
+  var names = [t.literal("exports")];
+  if (this.passModuleArg) names.push(t.literal("module"));
+  names = names.concat(this.buildDependencyLiterals());
   names = t.arrayExpression(names);
 
   // build up define container
 
   var params = _.values(this.ids);
+  if (this.passModuleArg) params.unshift(t.identifier("module"));
   params.unshift(t.identifier("exports"));
 
   var container = t.functionExpression(null, params, t.blockStatement(body));
diff --git a/lib/6to5/transformation/modules/umd.js b/lib/6to5/transformation/modules/umd.js
index e23c7c6fc2..4f0ec24ce9 100644
--- a/lib/6to5/transformation/modules/umd.js
+++ b/lib/6to5/transformation/modules/umd.js
@@ -25,22 +25,31 @@ UMDFormatter.prototype.transform = function (ast) {
   // factory
 
   var ids  = _.values(this.ids);
-  var args = [t.identifier("exports")].concat(ids);
+  var args = [t.identifier("exports")];
+  if (this.passModuleArg) args.push(t.identifier("module"));
+  args = args.concat(ids);
 
   var factory = t.functionExpression(null, args, t.blockStatement(body));
 
   // runner
 
-  var defineArgs = [t.arrayExpression([t.literal("exports")].concat(names))];
+  var defineArgs = [t.literal("exports")];
+  if (this.passModuleArg) defineArgs.push(t.literal("module"));
+  defineArgs = defineArgs.concat(names);
+  defineArgs = [t.arrayExpression(defineArgs)];
+
+  var commonArgs = [];
+  if (this.passModuleArg) commonArgs.push(t.identifier("module"));
+  commonArgs = commonArgs.concat(names.map(function (name) {
+    return t.callExpression(t.identifier("require"), [name]);
+  }));
+
   var moduleName = this.getModuleName();
   if (moduleName) defineArgs.unshift(t.literal(moduleName));
 
   var runner = util.template("umd-runner-body", {
     AMD_ARGUMENTS: defineArgs,
-
-    COMMON_ARGUMENTS: names.map(function (name) {
-      return t.callExpression(t.identifier("require"), [name]);
-    })
+    COMMON_ARGUMENTS: commonArgs
   });
 
   //