CL600 CRJ FLT CREW HAS A TRACK AND HDG DEV DURING APCH TO MEM DUE TO ACFT EQUIP PROBS.

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CAPT WAS PF AND I WAS FO AND PNF ON ILS RWY 36R APCH AT MEM. APCH CLRED US TO DSND TO 2000 FT AND MAINTAIN A 330 DEG HDG UNTIL ESTABLISHED ON THE LOC AND CLRED US FOR THE APCH. THE CAPT SELECTED APCH MODE AND HE WAS LOC1/GS ARMED WHILE I WAS LOC2/GS ARMED. OUR RESPECTIVE NAV DISPLAYS BOTH CORRECTLY SHOWED THE 358 DEG INBOUND LOC COURSE AND THE AUTO-IDENT FOR THE LOC. I ALSO RECEIVED A CORRECT MORSE CODE IDENT FOR THE LOC. APCH CTL HANDED US OFF TO MEM TWR. APPROX ABEAM HADAN FIX; MY LOC2 CAPTURED WHILE HIS LOC1 STILL SHOWED A L DEFLECTION. I COMPARED MY LOC ALIGNMENT WITH THE FMS OVERLAY AND SHOWED WE WERE CTRED ON THE LOC. AS WE FLEW THROUGH THE RWY 36R LOC; THE CAPT'S LOC1 STILL SHOWED A L DEFLECTION AND DID NOT CAPTURE. I NOTIFIED HIM OF THE DEV L OF COURSE AND TWR QUERIED US ABOUT OUR ALIGNMENT. I TOLD TWR WE WERE GETTING ESTABLISHED AND THEN TOLD THE CAPT TO COME R. HIS LOC1 INDICATION STILL SHOWED A L DEFLECTION; HE CLICKED OFF THE AUTOPLT; REMOVED THE FLT DIRECTOR; AND HAND-FLEW THE ACFT BACK TO THE CORRECT COURSE. TWR QUERIED US AGAIN TO ENSURE WE WERE LINING UP FOR RWY 36R AND NOT RWY 36L. I RESPONDED THAT WE WERE SET UP FOR RWY 36R. THE CAPT AND I AGREED THAT HIS SIDE WAS SHOWING INCORRECT LOC1 DATA AS HE SHOWED FULL-SCALE L DEFLECTION WHILE LOC2 WAS NEARLY CTRED AND CONSISTENT WITH THE FMS COURSE OVERLAY. AT THIS POINT; WE XFERRED CTLS AND NOW I WAS THE PF. I HAND-FLEW THE APCH ON LOC2 RAW DATA. AT APPROX MCGHE FAF THE CAPT QUERIED TWR ON OUR LOC ALIGNMENT AND THEY STATED WE WERE ON COURSE. MY LOC2 CONTINUED TO SHOW US ALIGNED WHILE THE CAPT'S LOC1 SHOWED FULL-SCALE L DEFLECTION. SHORTLY BEFORE WE BROKE OUT OF THE CLOUDS; THE CAPT AGAIN ASKED TWR IF WE APPEARED TO BE ON COURSE AND THEY RESPONDED THAT WE WERE. AS WE BROKE OUT OF THE CLOUDS AT ABOUT 300 FT AGL; WE WERE ALIGNED R OF RWY 36R. I THEN OBSERVED A YELLOW LOC FLAG ON MY HSI. AT ABOUT THE SAME TIME; WE RECEIVED AN 'EFIS COMP MON' CAUTION INDICATING OUR RESPECTIVE PFD HDGS WERE MISALIGNED. THE CAPT SAW THE RWY 36R APCH LIGHTS TO OUR L; TOOK CTL OF THE ACFT AND LANDED THE ACFT SAFELY. ONCE AT THE GATE; OUR COMPANY'S AVIONICS TECHNICIAN STATED THIS ACFT HAD A HISTORY OF LOC PROBS ON APCHS. IN LOOKING BACK ON THE EVENT; ONE THING WE COULD HAVE DONE BETTER WAS AFTER XFERRING CTL OF THE ACFT; I SHOULD HAVE INSTRUCTED THE CAPT TO RE-SELECT APCH MODE WHICH WOULD REACTIVATE THE FLT DIRECTOR. THEN WE COULD HAVE ACTIVATED THE AUTOPLT TO GIVE US A BETTER IDEA OF THE SIGNIFICANCE OF THE PROB BY BOTH OF US MONITORING THE VARIOUS INDICATIONS. HAD THE LOC2 INDICATIONS BEEN CORRECT; WE COULD HAVE EASED OUR WORKLOAD FROM THE FAF TO LNDG (WHICH APPEARED TO BE THE CASE AT LEAST UNTIL SHORT FINAL). OTHERWISE; HAD WE SEEN THE LOC2 DATA WAS ALSO INCORRECT COMPARED WITH THE FMS COURSE OVERLAY; WE WOULD HAVE REMOVED THE AUTOMATION AND CONDUCTED A MISSED APCH. AS IT WAS; HAND-FLYING A RAW DATA APCH WORKED OUT SUCCESSFULLY.