CAPT OF A B737-300 TAXIED TO AND ONTO THE WRONG RWY RESULTING IN TWR SENDING ANOTHER ACFT AROUND AND HOLDING HIM IN POS FOR SUBSEQUENT TKOF ON THAT RWY.

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COMING INTO JAX WE SHOT AN ILS TO RWY 7 WHERE THE WX WAS APPROX 500 FT OVCST AND 2-3 MI VISIBILITY. WE DEPLANED OUR PAX AND ENPLANED OUR FLL PAX. AFTER PUSHBACK WAS COMPLETED; I CALLED JAX GND 'READ FOR TAXI.' THE JAX GND CTLR GAVE US TAXI CLRNC TO RWY 13. HE GAVE US NO SPECIFIC TAXI INSTRUCTIONS ON HOW TO TAXI TO RWY 13; SO WE PROCEEDED TO TAXI VIA TXWY J AND TXWY A. AS WE WERE TAXIING; WE WERE RUNNING OUR NORMAL CHKLISTS. AS WE WERE APCHING THE DEP ENDS OF RWYS 13 AND 7; WHICH ARE IN CLOSE PROX; I CALLED THE JAX TWR AND INFORMED THEN THAT WE WOULD BE READY FOR TKOF AT THE END OF THE RWY AND THAT WE WOULD HOLD SHORT. AT THAT TIME; WHILE WE WERE STILL ROLLING; THE JAX TWR CTLR CLRED US FOR TKOF ON RWY 13 AND INSTRUCTED US TO FLY RWY HDG. AT THAT TIME I PROCEEDED TO COMPLETE THE REMAINDER OF THE CHKLIST; AND WAS DOUBLECHKING THAT EVERYTHING WAS PROPERLY SET UP FOR TKOF AND DEP. WHEN I LOOKED UP AFTER COMPLETING MY DUTIES; I REALIZED THAT WE HAD PROCEEDED ACROSS THE RWY 7 HOLD SHORT LINE; AND SAID TO THE CAPT THAT I THOUGHT THAT THE JAX TWR CTLR HAD CLRED US FOR TKOF ON RWY 13. HE SAID THAT HE THOUGHT THAT THE TWR CTLR HAD CLRED US FOR TKOF ON RWY 7. AT THAT TIME I TOLD THE CAPT THAT I WAS GOING TO CALL THE TWR BACK TO VERIFY WHAT RWY WE HAD BEEN CLRED FOR TKOF ON; AND WE HELD OUR POS. BEFORE I COULD CALL THE TWR; THEY CALLED US; AND ASKED US WHAT WE WERE DOING ON RWY 7. THE CAPT THEN ADVISED THE TWR THAT HE THOUGHT THAT WE HAD BEEN CLRED FOR TKOF ON RWY 7; AND ASKED THE TWR CTLR WHAT HE WANTED US TO DO. THE TWR CTLR TOLD US TO HOLD OUR POS ON RWY 7. APPROX 1 MIN LATER; THE TWR CTLR CLRED US FOR TKOF ON RWY 7; AFTER WHICH WE MADE A NORMAL DEP. I BELIEVE THAT ONE OF THE CONTRIBUTING FACTORS TO THIS OCCURRENCE WAS THE FACT THAT WE NEVER RECEIVED SPECIFIC TAXI INSTRUCTIONS ON HOW TO PROCEED TO RWY 13. I BELIEVE THAT ANOTHER CONTRIBUTING FACTOR TO THIS OCCURRENCE WAS THAT THE GND AND TWR CTLRS SEEMED TO NOT BE WATCHING OUR PROGRESS TO THE RWY AND OUR PROGRESS ONTO THE RWY. SOME POSSIBLE CORRECTIVE ACTIONS TO PREVENT AN OCCURRENCE OF THIS TYPE FROM HAPPENING AGAIN WOULD BE AS FOLLOWS: 1) GIVE SPECIFIC TAXI INSTRUCTIONS ON WHICH TXWYS TO TAKE TO THE ASSIGNED RWY. 2) CTLRS MONITORING THE ACFT MOVEMENT CLOSER TO HELP PREVENT CONFLICTS OR MISTAKES.