I have an applet running in a browser.
Sometimes when I try to close the browser ( Firefox & IE ) they freeze.
The last line I see in the jvm output is “basic: Stopping applet…”
What methods of my applet is the jvm trying to call when it is stopping the applet?
stop() and destroy()
Safari calls stop() when you switch to a different tab, and calls start() again when you switch back. All the other browsers call stop() when you leave the page that contains applet, either by closing the tab or navigating to a different page.
In all browsers (AFAIK), when you leave the page, stop() is called followed by destroy().
Yes, the browsers became naughty and stopped doing that 
As for the freezing, what is your applet actually doing? That just shouldn’t happen.
Why is this in the J2ME forum?
Well in fact this is one of those cases where the plugin or the browser is buggy. One of those cases why applets are hated so much.
Could you please update to the latest version of java (1.5.0_12 or 1.6.0_1) and see if the problem is still there.
If its still there could you please file a bug-report at http://bugs.sun.com/bugdatabase/index.jsp - with detailed informations about your system (versions of browsers, installed service packs, …).
lg Clemens