When the 1976 2 Dollar bills were being issued there was a story going around that if you took a new bill on the first day of issue to the post office and had it postmarked that later it would be more valuable? I had two postmarked and both were put up and have not been handled or circulated. I received these from a bank in San Francisco. Any idea if postmarked bills on first day of circulation are more valuable?

How could they be postmarked without being handled?

And if they came from a bank.. then they were actually in circulation AND handled by a number of people.

Uncirculated Bills and coins come directly from the mint. And typically would have been sealed in something. Newly issued money is not the same as uncirculated money.

Not that they are worth much if anything over face value...and the postmark would actually take away from part of that.

Go to eBay and compare yours to what others are getting or asking.

1976 postmarked $2 bill | eBay

From the eBay listing, it appears many people asking for a lot of money, but the only ones I saw bids on, were for about 2.25 to 3.00 per bill.

I will agree, as the age, a truly non-circulated bill should have higher value than one that was stamped.