A300
Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Situational Awareness
Aircraft Equipment Problem Critical; Flight Deck / Cabin / Aircraft Event Smoke / Fire / Fumes / Odor
Aircraft Aircraft Damaged; Flight Crew Overcame Equipment Problem; General Maintenance Action
Aircraft
On landing rollout Runway XXL; after thrust reverser deployment; Engine #1 rolled back and shutdown. Taxied off runway and proceeded to taxi [Taxiway] XX; [Taxiway] XY. [Taxiway] XZ; and ]taxied across Runway XY at [Taxiway] XA; then right on Taxiway XB to spot.  Enroute coordinated with Maintenance for tow in to gate since operating with only one engine. After check in with Ramp Tower; received call from them that we had a engine tail pipe fire. We had no indications of an engine #1 fire in the cockpit; but immediately decided to pull fire handle for engine #1; then fired bottle #1. After 30 sec; Ramp Tower indicated that the tail fire was not out; so we fired bottle #2. Fire crew on scene then stated that the fire was out. We were then towed in to gate.
After landing on [Runway] XXL at ZZZ and during the roll out the #1 left engine began to roll back and shut down. We taxied in on one engine via [Taxiway] XX; [Taxiway] XA; [Taxiway] XZ crossed [Runway] XY/XZ left onto [Taxiway] XB and turned into the ramp. The Ramp Tower informed us that the left #1 engine had flames protruding out the rear. We had no indications in the cockpit but being prudent we elected to pull the fire handle and initiate the extinguishing bottle #1. We waited for 30+ seconds and the Tower let us know that it appeared to still be on fire so we fired the 2nd bottle. Ramp Tower had asked if we wanted Fire and Rescue summoned to which we said yes and when they arrived they let us know that there were no more indications of fire. We then coordinated and was towed into gate.
A300 flight crew reported while taxiing to gate Ramp advised them of fire on the number 1 engine.