A CL65 CAPT DEVIATED FROM THE CLEARED COURSE WHEN HIS FMS MALFUNCTIONED.

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IN CRUISE; AT FL270 ALONG J51; 100 NM S OF FAK; THE FMS HAD LOST ITSELF WITH RESPECT TO ITS POS. A MESSAGE FLAGGED US 'CHK POS' MEANING CHK POS; WHERE I UPDATED THE POS VIA THE UPDATE POS FUNCTION ON THE FMS. I HAD TO DO THIS ABOUT 3 DIFFERENT TIMES. THERE WAS NOT A NEED TO RPT THE FMS AS FAILED BECAUSE I COULD SUCCESSFULLY UPDATE THE POS. I BELIEVE ON THE 3RD TIME THIS OCCURRED WE WERE ON A PRETTY LARGE INTERCEPT ANGLE TO REINTERCEPT THE AIRWAY WHEN ATC ASKED US OUR HDG; TO WHICH I HAD REPLIED WE WERE REJOINING THE AIRWAY AND THAT I WAS HAVING A LITTLE TROUBLE WITH THE FMS NAV AND THAT I WAS CORRECTING IT. I DO NOT KNOW THE EXACT DISTANCE WE WERE OFF COURSE; BUT I DO KNOW IT WAS LESS THAN 10 MI FOR CERTAIN; BUT I AM PRETTY SURE THAT IT WAS 5 NM OR LESS. MY NAV SCREEN WAS ZOOMED OUT TO THE 80 NM SCALE MAKING SMALL DISTANCES DIFFICULT TO DETERMINE. WHEN I GOT THE FMS POS CORRECTED I ZOOMED IN ON THE NAV SCREEN AND IT ONLY SHOWED ME ABOUT 3 NM OFF COURSE. I ASKED ATC IF THERE WERE ANY ISSUES OR PROBS WITH OUR NAV PROB; AND HE SAID NO; AND THANKED ME FOR ASKING. NO OTHER ISSUES OCCURRED UNDER THIS PROB. THIS PROB COULD HAVE BEEN AVOIDED IF ALL TURBINE PART 121 CARRIERS WITH FMS WERE REQUIRED TO HAVE GPS TO AID THE FMS IN PINPOINT ACCURACY NAV.