A B737-300 FLC CLBS TOWARDS FL370 WHEN THE CTLR HAD CLRED THEM TO FL270. FLT PLAN FILED HAD REQUESTED FL270.

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ON CLBOUT PASSING FL220 WE WERE GIVEN A FREQ CHANGE TO ZOA (HI). WE CONTACTED CTR AND WERE GIVEN A CLRNC TO CLB TO AND MAINTAIN FL370. WE HEARD FL370 AND READ BACK FL370; AND CONTINUED TO CLB TO FL370. OUT OF FL283; ZOA CALLED AND SAID; 'SAY ALT.' WE RESPONDED WITH 'FL283' AND WERE TOLD TO MAINTAIN FL270. WE DSNDED TO FL270. WE ASKED IF THERE WAS A CONFLICT. CTR RESPONDED THAT THERE WAS NO CONFLICT. THIS PARTICULAR LEG; SMF TO LAS; OCCURRED ON THE LAST DAY OF A 3 DAY TRIP. IT WAS THE NEXT TO THE LAST LEG IN A 3 DAY TRIP WITH 17 LEGS. WE WERE BOTH TIRED; AND FEEL THE 'CUMULATIVE EFFECT' OF THE PREVIOUS 2 LONG DAYS PLAYED A ROLE IN OUR FATIGUE AT THE END OF THIS THIRD DAY. OUR FILED ALT BY OUR DISPATCH WAS FL270. IT CROSSED MY MIND WHEN I HEARD THE CLRNC TO FL370 THAT WE SHOULD CHK WITH CTR TO VERIFY FL370 AND NOT FL270. NEXT TIME I WILL. HOWEVER; THERE ARE TIMES WHEN CTR WILL GIVE US A DIFFERENT ALT THAN FILED; SOMETIMES HIGHER SOMETIMES LOWER. BECAUSE THEY (CTR) KNOW THAT THE RIDE IS BETTER UP HIGHER OR WX IS SUCH THAT A HIGHER OR LOWER ALT WOULD BE BETTER. BUT I; WE; HEARD FL370 OR THOUGHT WE DID; SO MUCH SO IN FACT THAT WE READ BACK FL370 AND CONTINUED THE CLB TO FL370. NEXT TIME; QUESTION THE CTLR WHEN 'FILED' IS DIFFERENT THAN 'HEARD' IF THEY OFFER NO EXPLANATION FOR DIFFERENT ALT. IN THIS CASE; NO ONE SAID ANYTHING. SUPPLEMENTAL INFO FROM ACN 416078: WE DISCUSSED THE FACT THAT WE HAD ONLY FILED TO CRUISE AT FL270; BUT WE BOTH CLRLY HEARD THE CTLR AND UNDERSTOOD HIM TO SAY 'CLB TO FL370;' SO WE COMPLIED WITHOUT QUESTION.