One Laptop - two completely separate workspaces

[Slavei Karadjov]

I am a newbie in the Linux world. I have a laptop(old IBM T42 with Ati
video card) + external monitor, mouse and keybord. The external
devices work with my laptop. What I want to do is to have completely
separate X sessions, so that I can work using the external monitor,
mouse and keyboard completely separate without interfering the work on
the LCD. Something like working on one laptop and having two separate
workspaces.

Is this possible?

Thank you in advance for you help.

Regards,
 S K