COMMUTER FLC DOES NOT MAINTAIN RWY HDG AFTER DEP. FO HAD TOLD CAPT 'CLRED AS FILED' AND BEGAN TURN AFTER AIRBORNE. ATC QUERIED FLC REGARDING HDG.

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I WAS THE CAPT OF A COMMUTER FLT BTWN SPENCER; IA; AND SIOUX CITY; IA. I WAS IN THE TERMINAL WHEN MY FO PICKED UP OUR CLRNC TO SUX. I CAME BACK OUT TO THE ACFT; GOT READY AND THEN WE TAXIED FOR DEP OFF RWY 12. AS WE WENT THROUGH OUR CHKLIST; I ASKED THE FO WHAT OUR CLRNC WAS TO SUX. HE REPLIED THAT WE WERE CLRED TO 4000 FT AND AS FILED TO SUX. THE FO WAS THE PF AND WE DEPARTED OFF RWY 12. AFTER 1500 FT AGL THE FO HAD JUST STARTED TO MAKE A R TURN AS I CONTACT ZMP. ZMP ASKED US IF WE WERE ON RWY HDG AND I REPLIED THAT WE WERE. AS THE FO ROLLED BACK ON RWY HDG MSP SAID WE WERE RADAR CONTACT AND CLRED TO 10000 FT AND CLRED ON COURSE THROUGH 6000 FT. MSP THEN TOLD US TO EXPEDITE OUR CLB AND VERIFY THAT WE WERE STILL ON RWY HDG. I LOOKED DOWN AND THE FO HAD DRIFTED R OF HIS COURSE; SO I TOLD HIM TO EXPEDITE AS QUICK AS HE COULD AND TO GET BACK ON HIS RWY HDG. WE WERE EMPTY; SO WE CLBED VERY QUICKLY; AND I TOLD MSP THAT WE WERE CURRENTLY THROUGH 6500 FT AND TURNING ON COURSE. I BELIEVE THIS SIT OCCURRED BECAUSE OF THE FO NOT PAYING ATTN TO HIS DUTIES OR WHAT WAS GOING ON AROUND HIM. I LOOKED AT THE CLRNC HE HAD WRITTEN DOWN AND IT SHOWED THAT WE SHOULD EXPECT ON COURSE 5 MINS AFTER DEP. SO HE RECEIVED THE RIGHT CLRNC; BUT TOLD ME THAT WE WERE CLRED AS FILED. I THINK TO PREVENT THIS IN THE FUTURE; I WILL TRY TO BE ON BOARD WHEN WE GET OUR CLRNC AND MAKE SURE IT IS WRITTEN OUT FULLY AND LEGIBLY SO WE CAN BOTH REVIEW IT OR ELSE TRY TO GET THE CLRNC MYSELF.