Somehow session type option in slim does not work in slim. When pressing F1 as indicated nothing happens. On the other hand, I have not found other ways to change window manager to xfce or gnome which I installed. In window manager menu in for example fluxbox, there are not xfce or gnome. What to do?

Post /etc/slim.conf and your .xinitrc files.

You might simply need to add them.

If you have a fairly powerful box to run xfce and/or gnome you might be better off running gdm instead of slim login manager. You may need to reconfigure login manager

as root dpkg-reconfigure gdm (or slim)

Installing gdm (gdm3) solved my problem. Now I can login to all the window managers installed. Thanks a lot again!