A B737-800 PILOT REPORTS OF AN UNCOMMANDED #2 ENG SURGE DURING AUTOTHROTTLE EXCEEDING N-1 LIMITATIONS SEVERAL TIMES.

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DURING CLB; JUST PRIOR TO LEVELOFF AT FL340; WE EXPERIENCED AN ENG SURGE THAT CAUSED THE ACFT TO MOVE AND ALSO THE ENG INSTS. THE #2 ENG N1 GAUGE DID EXCEED A LIMITATION SEVERAL TIMES IN A SHORT TIME PERIOD (MAYBE 10 SECONDS). I KNOW THIS BECAUSE I SAW IT TURN RED BUT I DIDN'T SEE HOW HIGH THE N1 GOT. I DISCONNECTED THE AUTOTHROTTLE AND RETARDED THE THRUST LEVER SLIGHTLY. AT THE SAME TIME WE LEVELED OFF (AUTOPLT STILL ON). THE ENG QUIT SURGING AND RESUMED NORMAL OPS. WE FOLLOWED THE ENG LIMIT/SURGE/STALL CHKLIST TO ITS COMPLETION. AFTER THAT WE DISCUSSED THE SITUATION WITH MAINT CTL. I WAS CONCERNED THAT WE HAD EXCEEDED A LIMITATION ON THE ENG AND EVEN THOUGH WE DIDN'T KNOW HOW MUCH THAT WAS; I WAS CONCERNED ABOUT ENG HEALTH LATER IN THE FLT ALTHOUGH ALL INDICATIONS WERE VERY NORMAL WITH ALL PARAMETERS EVENLY MATCHED TO ENG #1. AFTER CONVERSATIONS WITH MAINT CTL AND DISPATCH; WE DECIDED TO CONTINUE TO ZZZ. THE FLT CONTINUED UNEVENTFULLY. I WAS LATER INFORMED BY THE LEAD MECH THAT MET THE PLANE THAT THE ENG DID EXCEED N1 LIMIT TO SUCH A DEGREE THAT THE ENG NEEDED TO BE CHANGED. I'M CONCERNED THAT WE FLEW AN ENG THAT NEEDED TO BE CHANGED FOR AN ADDITIONAL HR. THE CHKLIST SHOULD BE AMENDED TO INCLUDE GUIDANCE ON EXCEEDING LIMITATIONS THAT WOULD HAVE US LNDG SOONER RATHER THAN SIMPLY 'CHKLIST COMPLETE.' FLYING TO DEST AFTER EXCEEDING AN ENG LIMIT.