How could I use Jython threads as they were Java threads?

Well, putting aside the fact that you are calling the start() method from within the run() method, which is a really bad idea because once a thread is started, if you attempt to start it again you will get a thread state exception, setting that aside, the problem is, most probably, that you are using Jython threading library and not Java's.

If you make sure to import as follows:

from java.lang import Thread, InterruptedException

Instead of

from threading import Thread, InterruptedException

And if you correct the problem I cited above, chances are that your code will run just fine.

Using the Jython's threading library, you would need to change the code a bit, somewhat like:

from threading import Thread, InterruptedExceptionimport timeclass Cycle(Thread):    canceled = False    def run(self):        while not self.canceled:            try:                print "Hello World"                time.sleep(1)            except InterruptedException:                canceled = Trueif __name__ == '__main__':    foo = Cycle()    foo.start()

Which appears to work for me.