Large Transport; Low Wing; 2 Turbojet Eng
Flight Crew Air Transport Pilot (ATP)
Communication Breakdown; Situational Awareness
ATC Issue All Types; Conflict Airborne Conflict
Flight Crew Took Evasive Action
Environment - Non Weather Related; Procedure
Cleared to FL240. Between FL230 and FL240 received 'TRAFFIC' alert followed by 'ADJUST VERTICAL SPEED' followed again by 'DESCEND'. Crossing traffic at FL260. Closure rate may have been a factor. We were not advised by ATC of any traffic. We notified ATC of the RA and leveled normally at FL240. I am not sure if the traffic at FL260 had descended below FL260. To my knowledge; there was no loss of separation. Perhaps a notification from ATC about oncoming traffic would have been helpful.
An Air Carrier Captain reported that while climbing to FL240 TCAS alerted TRAFFIC; then ADJUST VERTICAL SPEED and finally DESCEND as a RA about traffic descending to FL260. ZDC did not issue traffic.