After landing, I noticed a truck on the side of the ramp and an individual waving at me. I taxied over to where the truck was, swung the airplane around 180 degrees, and with reverse thrust started backing towards the truck. I started through the aircraft shutdown procedures and when I pulled the mixtures to shut off, and as the number one engine came to a stop, I could hear a hissing noise similar to escaping air.
After liftoff, and initial climb out, everything was still performing as expected. We entered the clouds about the time of gear retraction. As soon as the gear was up, the number one engine started surging and the number two engine started backfiring. I briefed that we would continue straight ahead to the ADF and return for landing. I looked down at the ADF indicator and it was rotating continuously.