B727 ACFT IN CRUISE; FLC DISTRACTED BY RMI INDICATION; AUTOPLT DIDN'T HOLD ALT AND ACFT CLBED 500 FT BEFORE ATC CTLR CAUGHT ALT DEV.

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FLYING AN ACFT WITH AN OPEN WRITE-UP OF AUTOPLT WILL NOT ENGAGE; WE EXPERIENCED A NORMAL GND CHK AND ALT CAPTURE. WHILE WE WERE DISTRACTED WITH AN RMI ERRONEOUS INDICATION THE ACFT CLBED TO FL315 WITH THE GREEN ALT HOLD LIGHT ILLUMINATED. SUPPLEMENTAL INFO FROM ACN 403922: THE AUTOPLT TESTED CORRECTLY ON PREFLT AND THEN ENGAGED NORMALLY IN THE CLB OUT OF CVG. THE AUTOPLT CORRECTLY CAPTURED THE ALT AT FL310; AND MADE A NORMAL LEVELOFF. THE ALT HOLD LIGHT ILLUMINATED. APPROX 5 MINS AFTER LEVELOFF; WHILE THE CREW WAS TROUBLESHOOTING AN INOP #2 NAV NEEDLE; ZID REQUESTED US TO CONFIRM OUR FLT LEVEL. THE AUTOPLT ALT HOLD HAD FAILED AND THE ACFT HAD SLOWLY CLBED TO FL315. THE ALT HOLD LIGHT WAS STILL ILLUMINATED AND THE AUTOPLT DID NOT DISENGAGE. THE ACFT WAS THEN CORRECTED TO FL310 AND THE AUTOPLT DISENGAGED. DUE TO THE LATE HR OF THE FLT; FATIGUE MAY HAVE BEEN A CONTRIBUTING FACTOR; AS WELL AS THE DISTR OF OTHER MALFUNCTIONING SYS AT THE TIME. THIS WAS THE FIRST OF THIS TYPE OF OCCURRENCE I HAVE OBSERVED IN 10 YRS ON THIS TYPE ACFT. SUPPLEMENTAL INFO FROM ACN 403925: SO WAS MAKING A RPT TO COMPANY RADIO.