Date: 201912
Local time of day: 0601-1200
Location: ZZZ.Airport, US
Light: Daylight
Aircraft: B737-400
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Taxi
ATC / advisory: Ground ZZZ
Second aircraft: Medium Transport
Reporter organization: Air Carrier
Reporter function: Pilot Flying; Captain
Reporter qualification: Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Human factors: Communication Breakdown
Second reporter function: Pilot Not Flying; First Officer
Anomaly: ATC Issue All Types; Conflict Ground Conflict; Critical; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Ground Incursion Runway
Detector: Person Air Traffic Control
When detected: Taxi
Result: Air Traffic Control Issued New Clearance; Flight Crew FLC complied w / Automation / Advisory
Contributing factors: Human Factors
Primary problem: Human Factors

Narrative: This is a runway incursion event. The FO (First Officer) performed the landing on Runway XXR at ZZZ. As we exited the runway during a busy time for the FO; instructions were given for us to turn right on D; right on 'A'; hold short of Runway XY. Upon exiting the runway; the FO contacted Ground Control without being instructed to do so from the Tower. Ground Control instructed us to 'Cross Runway XY; 'A' 'H' to the cargo ramp. Apparently this was not coordinated with the Tower. The airplane was fully lit up for the crossing and we cleared left and right; but we did not see the business jet passing about 50-100 feet right in front of us. I think the Tower Controller came on the frequency just when we were about to cross and instructed us to HOLD SHORT! We abruptly stopped with the nose just past the hold short line and a few feet from the runway edge markings. We were then instructed to cross the runway; Alpha; Hotel; to the cargo ramp. We were informed of a possible pilot deviation and given a phone number to call. During the phone call; (which I think was the Tower Controller) he informed me that he had instructed us to hold short three times. We informed him that we were on Ground Control and that we had been cleared to cross. He reviewed the tapes and apologized.A very tired crew from our third hub turn; receiving instructions from the Controller at a busy time. The changed frequency without being instructed. Poor coordination with the Tower and Ground Controller (my opinion). Also we were not told the reason for the hold short; i.e.; 'hold short of XY for departing traffic; or; stay with me' which seems to be a standard. We are also absolutely sure that the Ground Controller cleared us to cross. Probably having our lights on and quick action stopping the plane made for a much better outcome.I informed the FO not to ever change to Ground Control after exiting the runway until instructed by the Tower. Apparently there is a misunderstanding of this procedure among many pilots. The controllers should always give a reason for a hold short clearance to give us situational awareness.


Second narrative: [Report narrative contained no additional information.]


Synopsis: B737 flight crew reported that poor coordination between Ground and Tower controllers resulted in a runway incursion.