B757 Undifferentiated or Other Model
Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Flight Crew Last 90 Days 119; Flight Crew Total 15875; Flight Crew Type 991
Conflict Airborne Conflict; Deviation - Altitude Excursion From Assigned Altitude
Flight Crew FLC complied w / Automation / Advisory
While level at FL340; we received a TCAS TA; followed by a TCAS RA. The TCAS display showed a target approximately 100 feet above us (+01). We initiated a descent; at which time the RA resolved (went away). We had deviated less than 200 feet from our original altitude (down to approximately 33850 [feet]). We returned to FL340 and reported to ATC. They said they did not show any aircraft in the area.
B757 Captain reported responding to a TCAS resolution advisory at FL340.