CL30 CAPT REPORTS SIGNIFICANT HEADING DISCREPANCIES BETWEEN HEADING SYSTEMS IN HIS ACFT DURING TAXI OUT. ONCE AIRBORNE PROBLEMS REAPPEAR CAUSING TRACK DEV.

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ON PREFLT AND TAXI OUT FOR TKOF AT MDW RWY 22L; OUR HDGS BTWN EFIS/FMS #1 AND #2 WERE SIGNIFICANTLY OFF THE TRUE MAGNETIC HDG. CAPT'S HDG WAS MORE THAN 30 DEGS INCORRECT; COPLT HDG INFO MORE THAN 20 DEGS INCORRECT. THIS WAS NOW THE SECOND TIME WE HAVE SEEN THIS OCCUR AT MDW IN THE LAST 90 DAYS. THE 'EFIS MISCOMPARE' CAS MESSAGE WOULD NOT CLR; NOR WOULD THE HDG WARNING FLAG PRIOR TO TKOF. AS PER THE AFM; WE MANUALLY SLAVED OUR HDGS TO 224 DEGS ON THE RWY JUST PRIOR TO TKOF. ALL WARNING FLAGS AND MESSAGES CLRED AND WE ELECTED TO LEAVE THE COMPASS IN DIRECTIONAL GYRO MODE UNTIL WE WERE AIRBORNE. (HAVING SEEN THIS MESSAGE ON THE GND BEFORE AT SEVERAL LOCATIONS; WE KNEW IT WAS PROBABLY GND INTERFERENCE CAUSING THE MAGNETIC DISRUPTIONS AND PLAYING HAVOC WITH OUR EFIS HDG SYS.) TKOF ROLL WAS NORMAL AND INITIAL CLB UNEVENTFUL. JUST PRIOR TO STARTING OUR R TURN FROM 220 DEGS AROUND TO AN INITIAL HDG OF 110 DEGS AS PART OF OUR VECTOR ON THE MIDWAY 6 DEP; I DE-SELECTED DIRECTIONAL GYRO MODE. EVERYTHING INITIALLY LOOKED BACK TO NORMAL AND I BEGAN MY CLBING R TURN. AS I ESTABLISHED US IN A CLBING R 30 DEG BANK; MY HDG DISPLAY ON PFD #1 STARTED SPINNING LIKE A TOP FOR A BRIEF SECOND OR TWO. AN 'EFIS MISCOMPARE' MESSAGE IMMEDIATELY TRIGGERED AN AMBER CAS MESSAGE ALONG WITH BOTH 'HDG' FLAGS ON BOTH PFD #1 AND #2. I QUICKLY NOTICED THAT MY HDG WAS NOW MORE THAN 180 DEGS IN ERROR; AND IT LOOKED LIKE THE COPLT'S MAGNETIC HDG INDICATION WAS INITIALLY CORRECT. I LEVELED THE WINGS AND SHALLOWED OFF OUR CLB AND ASKED MY CO-CAPT TO TAKE CTL WHILE I TROUBLESHOT THE PROB. CHICAGO DEP AT THE MOMENT ASKED US 'WHERE ARE YOU GOING;' BECAUSE WE WERE NOW HEADED SW INSTEAD OF OUT TOWARDS LEWKE; ALMOST AN E HDG FROM MIDWAY. WE QUICKLY STARTED BACK TOWARDS THE E; WHILE AVOIDING SOME TSTMS IN THE AREA; AND TOLD DEP WE WERE HAVING COMPASS INDICATION PROBS AND WERE TRYING TO FIGURE IT OUT. WE ROLLED OUT ON ABOUT A 060 DEG HDG AND LET THE MAGNETIC COMPASS STABILIZE. I TURNED OFF THE WINDSHIELD HEATERS AS PER AFM AND REENGAGED DIRECTIONAL GYRO MODE ON THE CAPT'S PFD AND MANUALLY SET MY HDG. ATC THEN ASKED WHAT HDG WE WERE CURRENTLY ON; I SAID 'ABOUT 060 DEGS.' HE AGREED AND THEN HANDED US OFF TO ZAU FOR FURTHER HANDLING. I THEN TOOK BACK CTL OF THE ACFT AND HAD MY CO-CAPT MANUALLY SLAVE HIS COMPASS HDG ON PFD #2. AFTER LEVELING OFF AT 14000 FT MSL AND STABILIZED FOR SEVERAL MINS; WE DE-SELECTED DIRECTIONAL GYRO MODE; BACK TO EFIS; AND EVERYTHING FROM THAT POINT WAS NORMAL AND UNEVENTFUL. ATC NEVER GAVE US ANY INDICATIONS OF A TFC CONFLICT OR ASSOCIATED PROBS FROM THE COMPASS ERROR. IN HINDSIGHT; I SHOULD HAVE WAITED UNTIL WE WERE ESTABLISHED ON OUR 110 DEG HDG IN STRAIGHT IN LEVEL; UNACCELERATED FLT PRIOR TO DE-SELECTING DIRECTIONAL GYRO MODE. THERE IS NO IMMEDIATE REASON FOR GOING BACK TO EFIS HDG WITHOUT BEING ESTABLISHED FIRST. LESSON LEARNED; AND I WAS JUST LUCKY I DID NOT CAUSE A TFC CONFLICT IN SUCH A CONGESTED AREA AS CHICAGO.