but I have the problem that sometimes the user start the application just after the wyUpdate has closed it, so the two process hang.
What do you mean they hang? What version of wyUpdate.exe & AutomaticUpdater are you using? Is there an error thrown? Are you running the wyUpdate from a service?
What can I do to check at the start up of my application if the wyUpdate is updating the application itself?
You can't -- just use the API correctly and handle all events. Also, make sure your app isn't locking up.