Narrative:

ATC cleared us to FL350. The FMC showed an 'opt' altitude of 35;100'. Passing through FL345 I noticed the aircraft had stopped climbing and had begun a shallow descent. The FMA had shown LNAV/VNAV speed and the thrust levers were at the appropriate power settings per the FMC. I selected V/south and began a climb at 400 fpm and reselected VNAV. Again the aircraft stopped climbing and then the autopilot disengaged with a flashing 'a' in the MCP speed window. At the time of disengagement; the speed was approximately 20 knots below barber pole but slightly faster than the FMC generated speed.I began to hand fly the aircraft and upon commencing a climb; I felt buffeting. I reduced the power but was unable to maintain altitude (100 - 200 fpm descent). ATC queried us as there was a potential conflict with another flight. I again tried to climb; but was unable due to the buffeting. At this point we received an RA to climb; but were unable to comply. The captain told ATC that we were unable to climb and that we needed a lower altitude. ATC then cleared us to FL340; and then to FL330.later that same flight; while on vectors for approach at 210 knots; clean configuration; level change; we again received a flashing 'a' in the MCP speed window. Upon landing; we contacted maintenance regarding the issue.as we were nearing the level off altitude of the aircraft; both the captain and I were diligently monitoring the aircraft. I think we reacted both timely and professionally.

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Original NASA ASRS Text

Title: B737 flight crew reported an inability to climb to FL350 which was 100 feet below the FMC optimum altitude. An attempt to climb in vertical speed resulted in the autopilot disengaging and a flashing 'A' in the MCP speed window. The inability to climb results in a TCAS RA which cannot be complied with.

Narrative: ATC cleared us to FL350. The FMC showed an 'OPT' altitude of 35;100'. Passing through FL345 I noticed the aircraft had stopped climbing and had begun a shallow descent. The FMA had shown LNAV/VNAV SPD and the thrust levers were at the appropriate power settings per the FMC. I selected V/S and began a climb at 400 fpm and reselected VNAV. Again the aircraft stopped climbing and then the autopilot disengaged with a flashing 'A' in the MCP speed window. At the time of disengagement; the speed was approximately 20 knots below barber pole but slightly faster than the FMC generated speed.I began to hand fly the aircraft and upon commencing a climb; I felt buffeting. I reduced the power but was unable to maintain altitude (100 - 200 fpm descent). ATC queried us as there was a potential conflict with another flight. I again tried to climb; but was unable due to the buffeting. At this point we received an RA to climb; but were unable to comply. The Captain told ATC that we were unable to climb and that we needed a lower altitude. ATC then cleared us to FL340; and then to FL330.Later that same flight; while on vectors for approach at 210 knots; clean configuration; Level Change; we again received a flashing 'A' in the MCP speed window. Upon landing; we contacted Maintenance regarding the issue.As we were nearing the level off altitude of the aircraft; both the Captain and I were diligently monitoring the aircraft. I think we reacted both timely and professionally.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.