Thank you to Sergey, Al, David. Your help brought me to better uderstand the behaviour of scheduled tasks and set up a solution.
I set up many scheduled task in W2000Server and W2003Server with an account created specifically for scheduling.
In those O.S. the scheduled tasks occur without regard to the currently logged account.
So now I realize it is not the same in XP Prof.
That is, only tasks scheduled by UserA will run when UserA is logged.
Tasks scheduled by UserB won't run when UserA is logged; better, they will run, but as a process than don't show, don't work and don't terminate!!
Moreover, only if the account has a password the scheduled task will run (a blank password won't activate the task).
Problems occur when the user changes periodically the password: it must be re-entered in each scheduled task.