An E-140 flight crew was unaware of a faulty ADC which was providing inaccurate altitude information to ARTCC controllers.

Narrative

I (PIC) was flying along at FL350 when I noticed that my airspeed was down [to] about 220 KTS. ATC notified us of an [aircraft] that was 12 o'clock and at FL340 and asked us if we have traffic in sight. He then asked us [our] altitude. My side (Captain's side) was reading about 34;600 FT; but I cross checked it with the standby and my First Officer's and both read FL350. Then ATC said we show you at 34;600 FT and I changed the transponder from transponder 1 to transponder 2; which is why they saw a jump in the altitude. We notified Dispatch through ACARS and they talked to MOC as we ran the checklist. While trying to figure out what this ADC was doing; at one point the airspeed was as low as 140 KTS. I think it was right above the white line; I remember that; but the other two airspeed indicators were reading around 250-260 KTS. Switched the ADC on my side from 1 to 2 then back again a couple of times. While running the checklist and talking to Dispatch; my ADC starting working correctly all of a sudden. Told Dispatch and was told to contact Maintenance Control when we land; which is what I did. I called them on my cell phone and told them what had happen and that the problem went away. They asked if I wrote it up and I told them no. They said [not to] worry about writing it up; it must have just been a 'gremlin' in the system. I told the other crew what had happened so they would keep and eye on it and then we went to the hotel. The altitude deviation was a faulty indication due to the problem with the #1 ADC. At no time were we off on our altitude because the autopilot was flying in cruise flight. The ADC was doing something stupid. I have been on this aircraft for about 9 years and have never seen anything like this. When I first noticed the ADC #1 messing up should have changed to ADC #2 when I noticed standby and First Officer's were reading correctly; but I was evaluating the problem and looking for traffic while flying the airplane.