Hi Nikhilesh,
If you mean a Flex-based AIR application when you say "desktop application", then the answer is: "Yes, you can test such applications with TestComplete". Please see the
Testing Flex-Based AIR Applications help topic and the rest topics of the
Testing AIR Applications section.
If you mean some kind of a desktop Windows application containing a WebBrowser control to which a web page with a Flex application is loaded and displayed at run time, the answer is: "Yes, you can perform functional testing of Flex contents in such applications, as well as test in-browser Flex applications running in Internet Explorer or Firefox". Please see the help topics of the
Testing Flex Applications section.
If you mean a Flex application running in a stand-alone version of Flash Player (Projector), the answer is: "No, testing of such applications is currently not supported by TestComplete. However, if you are really interested in testing such applications, please let me know about that. We will then consider implementing such support in TestComplete".
If this is not what you mean, please clarify what you need to test.
As for HTML web pages, TestComplete allows you to perform functional testing of such pages. For more information on this, please see the topics of the
Testing Web Applications section.