Shestakov,

Unfortunately I'm affraid you are on the wrong track. I think this incrementing thing has nothing to do with listener at all. I have stopped my listener and observed the number of "logons cumulative" in V$SYSSTAT and it keeps rising. So it is not connected to listener at all.

But I'm suspecting one other thing that might be causing this - Oracle's job queue processes. The number of cumulative logons in V$SYSSTAT increases by twice the number of JOB_QUEUE_PROCESSES every JOB_QUEUE_INTERVAL seconds even when there is no new connections to the database. When I started my database with JOB_QUEUE_PROCESSES = 0 the number of cumulative logons remains steady.