diff --git a/lib/jsduck/type_parser.rb b/lib/jsduck/type_parser.rb
index 67d3cce0a02d7d7d7970c5267a0178abb3d0c83e..08b0094c40fea2cc85db3e71fa1026c6728528e8 100644
--- a/lib/jsduck/type_parser.rb
+++ b/lib/jsduck/type_parser.rb
@@ -59,7 +59,7 @@ module JsDuck
     end
 
     #
-    #     <alteration-type> ::= <varargs-type> [ ("/" | "|") <varargs-type> ]*
+    #     <alteration-type> ::= <varargs-type> [ ("/" | "|") <varargs-type> ]*  [ "=" ]
     #
     def alteration_type
       skip_whitespace
@@ -78,6 +78,9 @@ module JsDuck
         skip_whitespace
       end
 
+      @out << "=" if @input.scan(/=/)
+      skip_whitespace
+
       true
     end
 
diff --git a/spec/type_parser_spec.rb b/spec/type_parser_spec.rb
index c88d277e3ca562e2f58bd156028b7704db6292eb..78872ea83b15d4fc8077b7dc64927166a42f27e0 100644
--- a/spec/type_parser_spec.rb
+++ b/spec/type_parser_spec.rb
@@ -173,12 +173,12 @@ describe JsDuck::TypeParser do
       parse("( String | Number )").should == true
     end
 
-    # This is handled inside DocParser, when it's detected over there
-    # the "=" is removed from the end of type definition, so it should
-    # never reach TypeParser if there is just one "=" at the end of
-    # type definition.
-    it "doesn't accept optional parameter notation" do
-      parse("String=").should == false
+    # This is handled mainly inside DocParser, when it's detected over
+    # there the "=" is removed from the end of type definition, so it
+    # should never reach TypeParser.  But additionally it can be used
+    # inside function type parameter list, so we need to support it.
+    it "matches optional parameter notation" do
+      parse("String=").should == true
     end
 
     it "matches single type argument" do
@@ -217,6 +217,18 @@ describe JsDuck::TypeParser do
       parse("function():Number").should == true
     end
 
+    it "matches function type with varargs" do
+      parse("function(...Number)").should == true
+    end
+
+    it "matches function type with nullable/non-nullable arguments" do
+      parse("function(!String, ?Number)").should == true
+    end
+
+    it "matches function type with optional argument" do
+      parse("function(Number=)").should == true
+    end
+
     it "matches function type with extra whitespace" do
       parse("function(  ) : Array").should == true
     end