Able to log in only once!

Hello,
I’m experiencing a strange problem.
As Admin, I created a new user (EDITOR) so my friends can add and edit posts and pages.
As long as I stay in the same browser window, it works fine. I manage to login with no problem.
When I open a new browser window, I get the following error message:
“You do not have sufficient permissions to access this page.“

To resolve this, I login with Admin, logout and login with the new user. Then it works again. Very strange behavior.
It’s like WordPress needed an Admin to “show” the way before a simple ‘Editor’ could login.

Would any of you have some suggestions on where the problem might be?

Phil