Starting second X session

I've installed Fedora Core 2 on a machine on my home network. X Windows (GNOME) is set up and works correctly, when I log in from the console.

However, when using Cygwin X from a different machine and trying to start an X session using startx it gives me the following error

That makes sense I guess because the fedora server already has an X session running at the console. I need to know how to create another X session for myself at a different computer.

I poked around about and found that the command
exec gnome-session helps somewhat in that an X session does get started, but many error messages pop up on the screen starting with:

Help would be appreciated.

Check this out:
http://voidmain.is-a-geek.net/redhat/fedora\_1\_terminal_server.html

Thanks Tux.

I followed the instructions from the link provided and it worked exactly the way I wanted it to.