HDG TRACK DEV BY A DC9 CARGO FLC WHEN THE CAPT FAILS TO NOTE A SLIGHT TURN TO THE R WHILE ON AUTOPLT DURING A RWY HDG DEP PROC FROM ABE; PA.

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DEPARTED ALLENTOWN ENRTE TO STEWART (NEWBURGH); NY. DEP CLRNC WAS TO FLY RWY HDG AND MAINTAIN 3000 FT. AFTER LEVELING OFF AT 3000 FT; THE AUTOPLT WAS ENGAGED. FOR SOME REASON; THE AUTOPLT STARTED A VERY GRADUAL R TURN. THIS WAS SO SLIGHT THAT IT DID NOT APPEAR ON THE ADI AS A TURN. THE FO WAS GETTING THE ATIS AND I WAS FLYING THE ACFT. I DID NOT NOTICE THE TURN UNTIL ASKED BY THE CTR CTLR WHY WE HAD TURNED OFF THE RWY HDG. I REPLIED TRUTHFULLY THAT I DID NOT KNOW WE HAD. THE CTLR THEN GAVE US A TURN BACK TOWARDS OUR ORIGINAL COURSE. A FURTHER PROB WITH THIS SIT IS THAT THE AIRSPD INDICATOR IS DIFFICULT TO SEE; AS IT IS PARTIALLY BLOCKED BY THE CTL YOKE. IF THE ATTITUDE DIRECTION INDICATOR DOES NOT SHOW THE TURN; AS IN THIS CASE; IT MIGHT NOT BE PICKED UP BY THE CREW. THIS WAS A NIGHT CARGO FLT THAT HAD BEEN DIVERTED TO ALLENTOWN AND WAS RUNNING BEHIND SCHEDULE. HAVING BEEN UP ALL NIGHT; FATIGUE CERTAINLY PLAYED A FACTOR. SUPPLEMENTAL INFO FROM ACN 561807: ASSIGNED A 060 DEG HDG BY THE TWR AND SWITCHED FROM APCH TO ZNY FREQ; WHO INFORMED US THAT WE COULD EXPECT HIGHER MOMENTARILY. THE CAPT; WHO WAS FLYING THE ACFT ON AUTOPLT; THEN DIRECTED ME TO OBTAIN THE ATIS INFO FROM OUR DEST (SWF; NY) AND ADVISED ME THAT HE WOULD MONITOR OUR PRIMARY RADIO FREQ WITH ZNY WHILE I OBTAINED THE ATIS. OUR ACFT BEGAN A SHALLOW R-HAND TURN/DRIFT FROM OUR PRIMARY HDG (STILL 060 DEGS); WHICH I ASSUMED TO BE A NEW HDG ASSIGNED BY ZNY. ZNY ASKED US WHY WE HAD DEVIATED FROM OUR PREVIOUS ASSIGNED HDG. MY COMPASS READ 085 DEGS. ZNY THEN ASSIGNED US A NEW HDG OF ABOUT 010 DEGS. THE CAPT; WHO WAS STILL FLYING ON AUTOPLT; THEN MADE AN ABRUPT TURN TO THE L TO COMPLY; AND APOLOGIZED TO ZNY CITING AN AUTOPLT DRIFT PROB. IN EFFECT; OUR AUTOPLT HAD MALFUNCTIONED AND STARTED A R-HAND DRIFT; EVEN THOUGH ALL CTLS WERE CTRED AND THE ACFT WAS RELATIVELY IN A TRIM CONDITION. I INCORRECTLY ASSUMED THAT THE CAPT WAS TURNING R TO COMPLY WITH A NEW ATC ASSIGNED HDG. OVERALL; I LEARNED THAT ONE HAS TO BE EXTREMELY VIGILANT WHEN ONE PLT IS FLYING THE ACFT AND COMPLYING WITH ATC INSTRUCTIONS; WHEN THE OTHER PLT IS BUSY COPYING OTHER INFO (ATIS).