B737-800 Captain reported the aircraft experienced uncommanded yaw events during cruise and descent. After the events; the flight continued to a normal landing.

Narrative

During cruise from ZZZ to ZZZ1 on Aircraft X at FL320 our aircraft encountered uncommanded yaw. We had been at cruise for about an hour and half. Our Flight Attendants (FA) were bringing our crew meal to us. At that time I left the flight deck to use the front lav. Just after stepping into the front galley with the flight deck door closed I felt the aircraft momentarily yaw as if a brief rudder input had taken place. I also saw the rear of the cabin move back and forth. On this flight I was the pilot flying (PF) Captain conducting OE 2 with a new FO. At the time I supposed and that the FO may have inadvertently touched the rudder pedal. After returning to the flight deck I asked if the FO if he had inadvertently touched the rudder pedal and he said that he did not. He did feel yaw as well. The flight continued uneventfully for the remainder of the cruise flight. We eventually step climbed to FL380. During decent somewhere below FL340 I noticed some left control wheel input. About 8 degrees or so. I added some Left Rudder input and the control wheel went back to zero. A few minutes after the aircraft had a sudden yaw again. This time it was much more pronounced. I used a small amount of right rudder to settle the aircraft. I again asked the FO if he had touched the rudder; and he responded no. We were discussing this when the FA called me and asked about the sudden tail movement. I told the FA we were trying to figure out what had happened and were working on it. I made a call to my dispatcher on the SAT Phone and just gave a heads up that we had some uncommanded rudder input and would be writing it up when we landed.The rest of the flight was uneventful with no other issues.At the gate I called my Dispatcher on the phone; Maintenance Control and the Duty Officer. [Decades] on the 737 NG and have never had uncommanded rudder control input. We encountered brief uncommanded rudder input once during cruise and once on decent. Flight landed successfully.