Date: 202103
Local time of day: 1801-2400
Location: ZZZ.ARTCC, US
Flight conditions: VMC
Aircraft: B757 Undifferentiated or Other Model
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Cargo / Freight / Delivery
Flight phase: Cruise
Airspace: Class A ZZZ
ATC / advisory: Center ZZZ
Second aircraft: Bombardier Learjet Undifferentiated or Other Model
Reporter organization: Air Carrier
Reporter function: Pilot Not Flying; Captain
Reporter qualification: Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Human factors: Communication Breakdown; Time Pressure; Situational Awareness
Second reporter function: First Officer; Pilot Flying
Anomaly: Conflict NMAC; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance
Detector: Automation Aircraft RA; Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Issued Advisory / Alert; Flight Crew Returned To Clearance; Flight Crew Took Evasive Action
Contributing factors: Environment - Non Weather Related; Human Factors
Primary problem: Human Factors

Narrative: While cruising at FL380; ATC advised us of traffic approaching us at 10 miles; opposite direction; FL370. My First Officer visually verified the traffic; but we did not relay this to ATC. Within 40 seconds from being notified we initially received a (TA) Traffic Advisory then immediately followed by an (RA) Resolution Advisory. My FO (First Officer) immediately disengaged the autopilot and flew the RA commands. As PM (Pilot Monitoring) I backed up my FO due to the high altitude deviation and climb. I immediately then advised ATC of our situation and actions. We initially climbed 700-800 feet before the RA commands stopped. Once stabilized and safe; we descended back to our cruise altitude of FL380. At one point the RA indicated the Learjet was within 200 feet of our aircraft. There was no communication from the [Learjet] or ATC concerning their deviation from assigned altitude.From what we can determine; the Learjet vacated its assigned altitude of [Flight Level] 370 and continued to climb. At no point did we hear any communications from them or ATC speaking to them. They could have been with another controller/Center frequency. Clearly; we were RVSM airspace.[Suggest] the Learjet not vacating its assigned altitude and ATC advising the Lear of [their] deviation would correct this situation. There was no acknowledgment or explanation to us for the deviation or error.


Second narrative: In cruise at FL380; ATC advised us of traffic at 1o'clock and 10 miles. I was able to gain sight of the called Learjet shortly. Within 40 seconds we had a Traffic Advisory (TA) followed by a Resolution Advisory (RA). I disengaged the autopilot and flew the RA commands to climb. The Captain as Pilot Monitoring advised ATC we were climbing for an RA. I maintained sight of the traffic and saw him pass just beneath our right wing and during the maneuver as little as 200 feet below us. Once stabilized with the traffic no longer a factor I descended down to our assigned altitude and reengaged the autopilot. At no point did we hear any communication to the Learjet from ATC regarding us as they were supposed to be at FL370.Better communication via ATC needed to both us and the Learjet if they saw any altitude deviations from the Learjet. Did not hear other than the initial traffic call was given and only to us.


Synopsis: Air Carrier flight crew reported a NMAC while at cruise altitude.