Medium Large Transport; Low Wing; 2 Turbojet Eng
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 162; Flight Crew Total 16490; Flight Crew Type 7988
ATC Issue All Types; Conflict NMAC; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued Advisory / Alert; Flight Crew FLC complied w / Automation / Advisory; Flight Crew Took Evasive Action
Human Factors; Procedure
We were on departure; level at 8;000 feet on ATC Vectors. ATC called traffic at our 10 o'clock. We visually acquired the traffic and at about that time; we received a TCAS TRAFFIC DESCEND. The First Officer promptly disconnected the auto pilot and followed TCAS guidance and I reported 'Maneuvering TCAS RA' to ATC. The small aircraft target (high wing single engine) then began descending. Shortly thereafter; we received a TCAS CLIMB NOW command which the First Officer promptly complied with. At this point; the small aircraft also changed path and started climbing.  The small aircraft maneuvered laterally away from us finally. Once we were clear of conflict; I told ATC we wished to report a Near Mid Air Collision; we re-engaged the autopilot and continued our flight. I messaged Dispatch and I verbally briefed Flight Operations after we landed.
Air carrier flight crew reported NMAC on departure climb.