A319, cruising at FL370, smooth conditions, ALT CRZ (and had been for more than 2 minutes, thus "soft altitude" hold), same problem both APs.
Very noticeable and uncomfortable for everyone on board. We used an manual thrust setting which seemed to improve the situation.
One other very strange item: in the following video look at the V/S versus the actual change of altitude on the tape (visible at 18 seconds and more clearly at the 1 minute mark). Related?
https://www.youtube.com/watch?v=9hk--9-fTlI
Very strange! Any ideas?