Narrative:

Climbing out of ZZZ1 going east; ATC gave us an off-course vector during the climb; then a few mins later back on-course and climb to FL210. TCAS advisory for traffic was received in the climb for traffic above us and apparently in transit to possibly a lower altitude. We had visual sighting of the aircraft. Our aircraft was on autoplt but climbing rapidly due to a light load. Around FL205 the MCP altitude acquired mode engaged followed shortly by a TCAS RA to adjust vertical speed. The autoplt was already leveling at FL210 so I let it continue the leveloff at the assigned altitude of FL210. We did not exceed or overshoot the altitude; but the aircraft above us received an RA and it climbed up into the path of another aircraft. It seems that the crossing of 3 aircraft at 3 different altitudes at just this moment was the cause of this one. About 5 mins or so later; on another ZZZ frequency; the ATC controller asked us if we had been level at the assigned altitude of FL210. The first officer confirmed it. All aircraft were assigned altitudes in a close approximation to each other. Normally there would probably have not been a problem; but I think our higher than normal climb rate triggered the TCAS system on the aircraft above us. Although nothing from my view was done incorrectly; it seems that having 3 aircraft converging while in transition could lead to future problems.

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Original NASA ASRS Text

Title: A B737 FLT CREW EXPERIENCED A TCAS RA WHILE LEVELING OFF AT THEIR ASSIGNED ALT.

Narrative: CLBING OUT OF ZZZ1 GOING E; ATC GAVE US AN OFF-COURSE VECTOR DURING THE CLB; THEN A FEW MINS LATER BACK ON-COURSE AND CLB TO FL210. TCAS ADVISORY FOR TFC WAS RECEIVED IN THE CLB FOR TFC ABOVE US AND APPARENTLY IN TRANSIT TO POSSIBLY A LOWER ALT. WE HAD VISUAL SIGHTING OF THE ACFT. OUR ACFT WAS ON AUTOPLT BUT CLBING RAPIDLY DUE TO A LIGHT LOAD. AROUND FL205 THE MCP ALT ACQUIRED MODE ENGAGED FOLLOWED SHORTLY BY A TCAS RA TO ADJUST VERT SPD. THE AUTOPLT WAS ALREADY LEVELING AT FL210 SO I LET IT CONTINUE THE LEVELOFF AT THE ASSIGNED ALT OF FL210. WE DID NOT EXCEED OR OVERSHOOT THE ALT; BUT THE ACFT ABOVE US RECEIVED AN RA AND IT CLBED UP INTO THE PATH OF ANOTHER ACFT. IT SEEMS THAT THE XING OF 3 ACFT AT 3 DIFFERENT ALTS AT JUST THIS MOMENT WAS THE CAUSE OF THIS ONE. ABOUT 5 MINS OR SO LATER; ON ANOTHER ZZZ FREQ; THE ATC CTLR ASKED US IF WE HAD BEEN LEVEL AT THE ASSIGNED ALT OF FL210. THE FO CONFIRMED IT. ALL ACFT WERE ASSIGNED ALTS IN A CLOSE APPROXIMATION TO EACH OTHER. NORMALLY THERE WOULD PROBABLY HAVE NOT BEEN A PROB; BUT I THINK OUR HIGHER THAN NORMAL CLB RATE TRIGGERED THE TCAS SYS ON THE ACFT ABOVE US. ALTHOUGH NOTHING FROM MY VIEW WAS DONE INCORRECTLY; IT SEEMS THAT HAVING 3 ACFT CONVERGING WHILE IN TRANSITION COULD LEAD TO FUTURE PROBS.

Data retrieved from NASA's ASRS site as of May 2009 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.