B737-700 CREW EXPERIENCES COMPRESSOR STALLS WHILE LEVEL AT 10000 FEET ON DEPARTURE AND RETURNS FOR SINGLE ENGINE LANDING.

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ON DEP OUT OF ZZZ LEVEL AT 10000 FT MSL; THE #1 (L) ENG EXPERIENCED A SERIES OF SUSPECTED COMPRESSOR STALLS. A SERIES OF THUDS ACCOMPANIED BY THE ACFT SLIGHTLY YAWING CONFIRMED THE FLUCTUATIONS INDICATED ON THE ENG INSTS. THE #1 THRUST LEVER WAS RETARDED TO IDLE AND THE SURGING AND STALLING STOPPED. THE 'B' FLT ATTENDANT CALLED TO SAY SHE HAD OBSERVED FLAMES SHOOTING OUT FROM THE BACK OF THE L ENG (DURING COMPRESSOR STALLS). AT THIS POINT WE XFERRED CTL OF THE ACFT TO ME. ATC CLRED US TO A HIGHER ALT AND WE REFUSED THE CLRNC AND TOLD THEM WE WOULD NEED TO RETURN TO ZZZ. I INSTRUCTED FO TO RUN THE 'ENG; FIRE; SEVERE DAMAGE; SEPARATION' CHKLIST. FOLLOWING THIS AND THE SUBSEQUENT ENG SHUTDOWN CHKLIST; WE SECURED THE ENG AND PREPARED FOR A SINGLE ENG LNDG BACK INTO ZZZ. I ALSO INSTRUCTED FO TO DECLARE AN EMER AND HAVE EQUIP STANDING BY AS A PRECAUTION. THE FLT ATTENDANTS WERE TOLD OF THE IMPENDING RETURN TO ZZZ AND TO 'SECURE' THE CABIN FOR ARR. AT NO TIME DURING THIS EVENT WAS THE LNDG OR SUCCESSFUL ROLLOUT EVER IN QUESTION. EVEN THOUGH AN EMER WITH ATC WAS DECLARED; IN MY JUDGEMENT; THIS EVENT DID NOT INDICATE THE PROBABILITY OF AN EVAC; HENCE; THE DECISION ON MY PART TO INSTRUCT THE FLT ATTENDANTS TO 'SECURE' VERSUS 'PREPARE' THE CABIN. WE WERE FEELING A BIT RUSHED BY ATC AS THEY IMMEDIATELY STARTED TO VECTOR US BACK TO THE VISUAL TO RWY 35R SO I ASKED FOR AN EXTENDED DOWNWIND. THIS GAVE US TIME TO FINISH THE APPROPRIATE CHKLISTS. AN UNEVENTFUL FLAPS 15 DEG LNDG WAS ACCOMPLISHED. DUE TO THE LIGHT LOAD AND LONG RWY; LNDG WT OR DISTANCE WAS NOT A CONCERN. CFR FOLLOWED US BACK TO THE GATE AND THE ACFT WAS SECURED. AN EXTERIOR POSTFLT INSPECTION DID NOT REVEAL ANY EXTERNAL DAMAGE AS FAR AS WE COULD SEE. ALSO; MAINT CTL INSTRUCTED ME TO QUERY THE FMC VIA THE MAINT INDEX TO CHK FOR ENG EXCEEDANCES. NONE WERE LOGGED. I HAD GOOD WX; A GREAT FO; AND ALL THE SUPPORT I COULD ASK FOR. UPON ARRIVING AT THE GATE MY FO BROUGHT TO MY ATTN THAT WE HAD SKIPPED PULLING THE FIRE HANDLE DURING THE EMER PROC. AS I RECALL; HE DID IN FACT CALL FOR THE ITEM AND I TOLD HIM TO 'STAND BY' AS ATC WAS VECTORING US AT THE SAME TIME AND ALSO ASKING ALL THE PERTINENT QUESTIONS LIKE FUEL AND SOULS ON BOARD. BOTTOM LINE IS IT WAS NOT ACCOMPLISHED. THE REST OF THE CHKLIST WAS SUCCESSFULLY COMPLETED. MISSING THIS ITEM DID NOT HAVE ANY MATERIAL EFFECT ON THE OUTCOME OF THE EVENT BUT STILL STINGS WHEN BROUGHT YOUR ATTN. AS FAR AS MISSING THE CHKLIST ITEM; IT WAS NOT INTENTIONAL. IT JUST HAPPENED TO COINCIDE WITH WHAT CLRLY WAS TASK SATURATION. I SHOULD HAVE TOLD ATC TO STAND BY AND NOT MY FO. WE SHOULD HAVE FINISHED THE CHKLIST UNINTERRUPTED AND THEN COMMUNICATED WITH ATC. LESSON LEARNED. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE REPORTER COULD NOT SUPPLY ANY ADDITIONAL INFORMATION AS TO WHY THE COMPRESSOR STALLS OCCURRED. HE DID NOT RECEIVE ANY ADDITIONAL INFORMATION FROM MAINTENANCE AFTER THE FACT.