FLC OF AN MLG ACR ACFT OPERATED ACFT CONTRARY TO THE ACFT MEL SINCE BOTH DME RADIOS WERE NOT WORKING DURING PRE TKOF CHKLIST.

Narrative

DURING ACFT PREFLT ON FIRST FLT OF THE DAY; BOTH DME'S WORKED NORMALLY. LATER; PRIOR TO PUSHBACK; BOTH DME'S DROPPED OFF; THEN CAME BACK ON; THEN OFF AGAIN. WE BOTH FELT THAT THE CHANCES OF BOTH DME'S ACTING THIS WAY WAS A XMITTER PROB; NOT A RECEIVER PROB. BECAUSE OF THIS; WE DECIDED TO PUSHBACK AND SEE IF A DIFFERENT LOCATION MIGHT SOLVE THE PROB. THE PROB; HOWEVER; STILL EXISTED AFTER PUSHBACK. I THOUGHT WE WERE 'DEAD IN THE WATER' AT THIS POINT AND TOLD THE FO TO CALL DISPATCH AND TELL THEM WE WERE RETURNING TO THE GATE. DISPATCH CONFIRMED WITH OUR MAINT PEOPLE AND ADVISED US THAT THEY COULD ONLY OFFER 1 DME; BUT SINCE WE WERE ALREADY 'ENRTE' ALL WE NEEDED TO DO WAS ADVISE ATC AND CONTINUE THE FLT (WX WAS CLR AT DEST AND FORECAST CLR AND FUEL WAS MORE THAN ADEQUATE). AFTER SOME DISCUSSION IN THE COCKPIT WE DECIDED THAT ALTHOUGH IT SOUNDED A BIT STRANGE; THEIR SOLUTION MIGHT WORK OK. WE ADVISED ATC; GOT AN AMENDED ALT OF FL230 AND COMPLETED THE FLT. I AM STILL NOT 100 PERCENT SURE WE VIOLATED ANY FARS BUT WE CERTAINLY STRETCHED THEM A BIT AND HINDSIGHT SAYS NOT TO DO THAT AGAIN. ALSO; THOUGH THIS PROBABLY IS QUITE REMOTE; BOTH DME'S DID FAIL AND HAD TO BE REPLACED.