Cart "Check out now" update displays "Thank you for your order" no updated cart

[sluc]

Updated a backup copy to VirtueMart 3.6.10 10211
The site does treat everybody as a guest! Registration is not enabled!
The first time order in a new session works OK.
Within the session starting a new order creates a problem in the cart display:
The "Check out Now" displays the message "Thank you for your order" instead of showing updated cart. If I manually update the cart-page it is displayed correctly and the order can be placed subsequently.
It is not template related (change to the beez does the same)
This problem was already there after the first 3.6 update!