HDG TRACK DEV IN AN OVERWATER OP DEVELOPS INTO A GROSS NAV ERROR. POS DEV.

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ACFT WAS DISCOVERED OFF COURSE TO THE N. A TURN S WAS MADE. SHORTLY THEREAFTER; I CHKED THE 'CROSS-TRACK' ON #2 INS AND FOUND IT TO BE 20 MI L. I WOULD ESTIMATE TOTAL OFF COURSE ERROR WAS 25-030 MI. INTENDING COURSE AT THE TIME WAS WBOUND FROM 57 DEG N 30 DEG W TO 55 DEG N 40 DEG W. AUTOPLT WAS DISCOVERED TO HAVE DEFAULTED FROM 'NAV' MODE TO 'HDG' MODE. HDG BUG WAS SET APPROX 30 DEG R OF INTENDED COURSE. ACFT WAS PLOTTED ON COURSE AT A POS OF APPROX 56 DEG 40 MIN N 32 DEG 00 W ABOUT 10 MINS PRIOR TO INCIDENT. AUTOPLT WILL DEFAULT FROM 'NAV' TO 'HDG' DURING A COURSE TRANSFER ON EFIS COURSE/HDG PANEL; BUT THIS FUNCTION WASN'T ACCOMPLISHED; SO I HAVE NO IDEA HOW AUTOPLT GOT TO HDG MODE. NORMAL PROC CALLS FOR ONE INS TO REMAIN IN 'COURSE' PAGE FOR A READOUT OF TRACK ERROR (DISTANCE FROM TRACK CTRLINE) I WAS CONDUCTING IOE TRAINING AT THE TIME AND GOING OVER VARIOUS FUNCTIONS OF BOTH INS UNITS; CATALOGS; DATA PAGES; ETC; SO NEITHER INS WAS IN COURSE PAGE. ON ANALOG TYPE ACFT HSI NEEDLE WOULD BE FULL SCALE DEFLECTION BEFORE BEING 10 MI OFF COURSE. ON EFIS PRESENTATION IN 'MAP' MODE AND 600 MI SCALE 20 MI OFF COURSE IS HARDLY NOTICEABLE. MY FLT DIRECTOR WAS SHOWING A COMMAND TO TURN L; BUT THIS IS NOT UNUSUAL WHEN THE OPPOSITE SIDE INS IS CTLING THE AUTOPLT. AN ANALOG ACFT IF THE AUTOPLT DEFAULTS FROM 'AUX NAV' (INS CTLING AUTOPLT) IT GOES TO 'TURN NOB' -- WHICH MAINTAINS CURRENT HDG. ON EFIS ACFT A DEFAULT GOES TO 'HDG' WHICH; DEPENDING ON BUG SETTING; CAN CAUSE A RAPID DEP FROM INTENDED COURSE; AS HAPPENED TO US. I BELIEVE INCREASING CREW AWARENESS TO THE FACT THAT AN 'OFF-COURSE' SITUATION WILL NOT BE DISPLAYED IN THE SAME DRAMATIC FASHION ON EFIS ACFT AS ON ANALOG TYPE DISPLAYS IS IMPORTANT. I ALSO BELIEVE CREWS TRANSITIONING TO EFIS EQUIP SHOULD BE AWARE OF THE IMPORTANCE OF SCANNING ADI NAV MODE DISPLAYS WHICH SHOW WHAT IS CTLING THE AUTOPLT. MY OWN INEXPERIENCE ON EFIS ACFT (APPROX 100 HRS) CONTRIBUTED TO THIS INCIDENT.