Electrical Questions? Ask an Electrician Online.
Hi, I'm Mike G and I'll be assisting you. The National Electrical Code which is followed by every municipal jurisdiction allows the GFCI device to protect the older circuits not having a ground. It is perfectly acceptable.
Let me add that the outlets protected need to be identified. There is a stick on label stating "GFCI protected - no ground" that should be on the outlets.
You're welcome. Enjoy your new home.