A CPR SMT WAS FACED WITH A SIMILAR CALLSIGN. ATC WAS NO HELP.

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ON JUL/THU/93 APPROX XA30; CAPT Z AND MYSELF PERFORMED A FLT FROM GREENVILLE; TX; TO WICHITA; KS. AFTER RECEIVING OUR CLRNC; WE DEPARTED GVT AND FOLLOWED OUR CLRNC INSTRUCTION. OUR REGISTRATION NUMBER WAS NX AND FROM THE TIME WE CHKED IN WITH ZFW THEY KEPT CALLING US NY. WE ASSUMED THAT IT WAS A NUMBER MISTAKE ON THEIR PART AND KEPT ADVISING THEM OF OUR CORRECT CALL SIGN OF SMT X NX. WE CONTINUED OUR FLT TO WICHITA AT FL260 AND APPROX HALF WAY TO WICHITA WERE SWITCHED TO ZKC. WE CHKED IN AGAIN AND THE CONFUSION OF CALL SIGNS CONTINUED. SMT X; NY; AND ADVISING THEM THAT WE WERE SMT X; NX. APPROXIMATELY 70 NM FROM WICHITA WE REQUESTED DSCNT. THEY CLRED US; SMT X NY; TO FL240. THEY KEPT US AT FL240 UNTIL APPROX 40 NM FROM WICHITA. WE AGAIN REQUESTED DSCNT AND THEY REPLIED SMT X NY DSND TO FL230 AND; AT THE SAME TIME; GAVE US A NEW ZKC FREQ. WE ACKNOWLEDGED SMT X NX DSND TO FL230 AND THE NEW ZKC FREQ AND ZKC NEVER CORRECTED OUR LAST XMISSION. WE CHKED IN WITH ZKC ON THE NEW FREQ ADVISING THEM THAT WE WERE AT FL230 AND AT THAT TIME WE HEARD AN SMT NY INBOUND TO WICHITA. ZKC ADVISED US THAT WE WERE AT THE WRONG ALT AND ON THE WRONG FREQ. ZKC NEVER ADVISED US THAT THERE WAS ANOTHER ACFT INBOUND TO WICHITA WITH AN ALMOST IDENTICAL CALLSIGN. WE FINALLY WERE GIVEN ANOTHER FREQ FOR ZKC AND RECOVERED AT WICHITA. ALSO; WHEN ZKC STATED WE WERE AT THE WRONG ALT; THEY NEVER CORRECTED US OR INFORMED US AT WHAT ALT WE WERE SUPPOSED TO BE. I BELIEVE WE WERE AT THE PROPER ALT BUT; THE WRONG SECTOR DID NOT KNOW OF OUR POS AND OUR INSTRUCTED ALT FROM THE PREVIOUS CTR. ALL THE CONFUSION COULD HAVE BEEN PREVENTED HAD CTR ADVISED US OF THE OTHER VERY SIMILAR CALLSIGN INBOUND TO WICHITA AT THE VERY SAME TIME.