Narrative:

I had requested a decent to FL350 which the pilot not flying relayed to ATC. We waited 5 - 10 minutes during which time center turned us to a northerly heading. Center then cleared us direct and to FL350. We turned FMS direct and started a gradual decent of 500 FPM. Reaching FL365 center asked us to expedite to FL350; I increased the rate of decent. After about three seconds ATC then asked us to turn 30 degrees right. He also asked another carrier's aircraft to turn 30 degrees to the left then corrected to the right. It was at this time ATC assigned us a heading of 180 and asked us to be at FL350 in 30 seconds; at this I replied 'that isn't happening' (regarding the decent). I disengaged the autopilot to increase our rate of turn. The controller then issued a new heading to the other flight and was asked to repeat by that crew. We were in a 30+ degree (of bank angle) descending right hand turn ATC was asking us to increase our rate of turn. We received an RA about two seconds after disengaging the autopilot at approximately FL355. At this time I held a 35 degree (bank angle) right hand turn and 1500+ FPM decent as commanded by the RA and confirmed by the pilot not flying until clear of the conflict. I estimate this took place in less than one minute. At no time did ATC issue a traffic advisory; warning or alert. The urgency to the situation was never conveyed from ATC to either flight crew. It is obvious that my initial slow decent contributed to this situation. However; if a request by ATC to be at FL350 by a certain time; such as 1 minute; or if we had been advised of the traffic at any time the decent would have either been delayed or expedited thus avoiding this situation.

Related reports:

Google
 

Original NASA ASRS Text

Title: A BE80 pilot reported a near miss with an air carrier aircraft at FL355. ATC issued a descent but requested an expedited descent only after the imminent conflict had already developed.

Narrative: I had requested a decent to FL350 which the pilot not flying relayed to ATC. We waited 5 - 10 minutes during which time Center turned us to a northerly heading. Center then cleared us direct and to FL350. We turned FMS direct and started a gradual decent of 500 FPM. Reaching FL365 Center asked us to expedite to FL350; I increased the rate of decent. After about three seconds ATC then asked us to turn 30 degrees right. He also asked another carrier's aircraft to turn 30 degrees to the left then corrected to the right. It was at this time ATC assigned us a heading of 180 and asked us to be at FL350 in 30 seconds; at this I replied 'that isn't happening' (regarding the decent). I disengaged the autopilot to increase our rate of turn. The Controller then issued a new heading to the other Flight and was asked to repeat by that crew. We were in a 30+ degree (of bank angle) descending right hand turn ATC was asking us to increase our rate of turn. We received an RA about two seconds after disengaging the autopilot at approximately FL355. At this time I held a 35 degree (bank angle) right hand turn and 1500+ FPM decent as commanded by the RA and confirmed by the pilot not flying until clear of the conflict. I estimate this took place in less than one minute. At no time did ATC issue a traffic advisory; warning or alert. The urgency to the situation was never conveyed from ATC to either flight crew. It is obvious that my initial slow decent contributed to this situation. However; if a request by ATC to be at FL350 by a certain time; such as 1 minute; or if we had been advised of the traffic at any time the decent would have either been delayed or expedited thus avoiding this situation.

Data retrieved from NASA's ASRS site as of April 2012 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.