Narrative:

This flight was in a -300 series that had the pmcs MEL'd inoperative and in the off position. Besides the additional power adjustments due to pmcs inoperative; ground ops; taxi; and takeoff were uneventful. At approximately 9500' MSL with climb thrust set and the autopilot on; the #1 engine began to roll back. The PF pushed the #1 throttle up as we first thought it could be due to the pmcs being off. The engine continued to roll back and the aircraft rolled and yawed left. The PF disengaged the autopilot as I coordinated for a level-off at 10;000' MSL and present heading. The #1 engine continued to roll back to approximately 50%. All other #1 engine indications indicated a roll back. However; as we began to retard the #1 thrust lever the engine began to return to commanded thrust. We decided to return to ZZZ and I coordinated for the return. We looked quick at the QRH and decided there wasn't an appropriate checklist to follow. We concluded the #1 engine had failed but restarted itself since the start switches were still on as the climb check had not yet been accomplished. Since the #1 engine was operating normally; a normal visual approach and landing was flown. No emergency was declared; however; emergency ground vehicles met the aircraft as we taxied normally to the gate. After review; however; we decided a flaps 15 approach and declaring an emergency would have been appropriate.

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Original NASA ASRS Text

Title: Dispatched with both PMCs [Power Management Computers] deferred the Flight Crew of a B737-300 encountered the apparent uncommanded failure and restart of the left engine during initial climb. They returned to their departure airport.

Narrative: This flight was in a -300 series that had the PMCs MEL'd inoperative and in the off position. Besides the additional power adjustments due to PMCs inoperative; ground ops; taxi; and takeoff were uneventful. At approximately 9500' MSL with climb thrust set and the autopilot on; the #1 engine began to roll back. The PF pushed the #1 throttle up as we first thought it could be due to the PMCs being off. The engine continued to roll back and the aircraft rolled and yawed left. The PF disengaged the autopilot as I coordinated for a level-off at 10;000' MSL and present heading. The #1 engine continued to roll back to approximately 50%. All other #1 engine indications indicated a roll back. However; as we began to retard the #1 thrust lever the engine began to return to commanded thrust. We decided to return to ZZZ and I coordinated for the return. We looked quick at the QRH and decided there wasn't an appropriate checklist to follow. We concluded the #1 engine had failed but restarted itself since the Start switches were still on as the Climb Check had not yet been accomplished. Since the #1 engine was operating normally; a normal visual approach and landing was flown. No emergency was declared; however; emergency ground vehicles met the aircraft as we taxied normally to the gate. After review; however; we decided a flaps 15 approach and declaring an emergency would have been appropriate.

Data retrieved from NASA's ASRS site as of April 2012 and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.