AN ACR MD11 FLC HAD THE ACFT LEAVE ITS ASSIGNED ALT AND START A CLB. NEITHER PLT NOTICED THE BEGINNING OF THIS PHENOMENON AND THE ALT ALERT DID NOT SOUND. THE FO NOTICED THE CLB AS THE ACFT PASSED FL355 AND THE FLC THEN RETURNED TO FL350 AND ADVISED THE ARTCC CTLR OF THE DEV. THE FLC IS CONVINCED THAT THIS WAS AN FMC MALFUNCTION; BUT ADMIT THAT THEY BOTH WERE UNDULY DISTR BY ROUTINE TASKS.

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WE HAD JUST LEVELED OFF FROM A STEP CLB FROM FL330 TO FL350. THE FO WAS BUSY WITH THE PLOTTING CHART AND I WAS BUSY WITH AN ACARS MESSAGE. THE FO NOTICED THE ACFT PASSING FL355 AND THAT FL360 WAS SET IN THE ALT CTLR ON THE FLT CTL PANEL. I ARRESTED THE CLB USING THE VERT SPD WHEEL; RESET FL350 IN THE ALT CTLR; AND SELECTED THE INIT PAGE ON MY MCDU. THE ALT BLOCKS ON THE MCDU INIT PAGE WERE ALL DASHES. MAX ALT REACHED DURING THE DEV WAS FL356. ALL NORMAL PROCS WERE FOLLOWED DURING THE STEP CLB AND WE ARE CONVINCED THE ACFT ENTERED AN UNCOMMANDED CLB THROUGH SOME TYPE OF FMS FAULT. THERE WERE NO ALT WARNINGS LEAVING FL350. WE ADVISED ZAN OF THE DEV. BOTH OF US ARE NEW TO 2 PLT TRANSPORTS. IF BOTH OF US HAD NOT BEEN DISTR WITH OTHER CHORES WE WOULD PROBABLY HAVE NOTICED THE DEV SOONER. IN THE FUTURE I WILL BE CERTAIN THAT EVEN IN CRUISE FLT THE PF WILL BE JUST THAT; AND ALL OTHER DUTIES WILL BE DELEGATED TO THE PNF. SUPPLEMENTAL INFO FROM ACN 375055: AFTER RE-ESTABLISHING FL350 WE NOTICED ON THE FLT PLAN INIT PAGE THAT THERE WERE DASHES IN THE CRUISE LEVEL FIELD. AFTER USING NORMAL PROCS (IE; ALT RESTR OF CLRED ALT IN ALT WINDOW) IN THE CLB; WE CONFIRMED PASSING FL340 FOR FL350 AND GOT THE ALT AURAL MESSAGE. WE LEVELED AT FL350 AND SHORTLY THEREAFTER THE DEV OCCURRED WITH NO ALT WARNING UPON LEAVING FL350. I AM CONVINCED THE FMS HAD SOME SORT OF FAULT. HAD THERE NOT BEEN THE DISTRS AT THAT TIME WE PROBABLY WOULD HAVE CAUGHT IT SOONER.