How to get process to start with GUI login and exit on GUI logout?

[Chris Green]

I have a background process that I want to start when I log into my
xfce session and I want it to exit when I log out of the session.

I thought that adding it to the list in the Session & Startup settings
would do this but the process doesn't exit when I log out from the
xfce session.  If I log out and then log back in to xfce I get
multiple copies of my process.

So, is there an easy/correct way to do this or do I need to add code
to my background process to manage things?

-- 
Chris Green