You may get any of the following messages ; UNABLE RNP, L GPS, R GPS, GPS depending on what the failure is but eventually the machine will transfer to DME/DME. If you're worried about nav accuracy and want to force it to DMEs you can switch the GPSs off. Bottom right of Prog Page 1 will tell you what mode it's using. DME/DME tuning is automatic (providing the MAN/AUTO switch on the VOR/DME controllers are set to AUTO). As above, they need to stay in AUTO.
Disclaimer - this is 75/76 specific. It's the only type I've flown and have no knowledge of any other Boeing or AB.
Hth