The problem arises when retailer systems fail to recognise the cards as valid. Like other computer systems, they were originally programmed to read only the final two digits of any given year, and crash when confronted with a reading of "00".
Visa and Mastercard's embargo on producing cards expiring in the year 2000 ended on 1 October last year. Barclays started producing 00 cards immediately, and now has over 1 million in use. The bank has so far had about 350 complaints from cardholders who have had their 00 cards rejected in shops and other outlets round the world, including 30 complaints in January.
Most other card issuers are also distributing 00 cards now, although none started as soon as Barclays. About four in 10 of the Barclays complaints arose in October. "Systems are becoming more compliant as time goes on," says the bank's Kirsty Robbie.
The big high street banks also supply their own credit card terminals to retailers, and have been busy updating those terminals to cope with the millennium bug for the past few years. Now, they say, all but a tiny handful of systems should be able to accept 00 cards with no problem.
But American Express is refusing to start producing its own 00 cards yet because it fears retail outlets worldwide will not be ready to accept them. Atalia DaSilva of American Express says: "I'm sure we'll issue year 2000 cards this year, but I don't know when. We want to make sure the merchants are ready to accept them in their point of sale devices. When a merchant's system rejects a card, it doesn't say why. It just rejects it. We want to avoid that happening."
Abbey National will not start issuing 00 cards till June this year, when its own systems testing is complete and it can be "completely confident" cards will not be rejected at point of sale. This has meant cutting the lifetime of its own cards to just 18 months - an expensive move for the bank.
NatWest started producing 00 credit cards about a month ago, and has since issued some 400,000, with no complaints so far. The bank has also been responsible for modifying the 170,000 terminals it has in shops and other retail outlets.
Last month two cases came to light where NatWest's modification of its terminals had failed. Both happened in Ikea branches, where customers' 00 cards were rejected, forcing staff to key in card details manually.
NatWest's Nick Gill says: "The upgrade had been put through for the year 2000, but there was a problem with the software. We realised that we'd need to write a new bit of software for it, because it was a bespoke terminal."
Mr Gill says the problem affected fewer than 100 of the terminals NatWest is responsible for, all of which have now been successfully dealt with. He says the bank is ahead of its rivals on year 2000 compliance.
Liz Phillips of the Credit Card Research Group says: "When you start issuing cards, you start finding the outlets where you're getting problems. It's often smaller retailers who've got a second-hand terminal which may not have been made Millennium compliant. The good thing is that the system behind the terminals is working OK."
Gerard Long, manager of Midland's year 2000 programme says: "It's where the terminals are owned by the retailer that there's an issue. They should go to their systems supplier and ensure they get a compliant version. There's only a small number of those out there and they are being addressed."
Some believe there will be more problems for cardholders using their plastic overseas than for those in the UK. Erica Harper of Royal Bank of Scotland says: "I suppose the test will be when the holiday season arrives. Internationally, I think there's likely to be more problems. People have always been advised to take lots of ways of paying for things when they go away, but this year I think that will apply all the more."
Visa divides the world up into six regions, all of which it says are 99 per cent or 100 per cent 2000-compliant. Visa's Matthew Talbot says: "We don't see any particular problem even in the most far-flung places. In the smaller, more remote, places, where Visa might be accepted, often you'll find a manual swipe machine, and no electronics at all."
If you should find your own 00 card rejected in a shop or restaurant, the owner should be able to phone whichever bank supplied his terminal to get authorisation, take a manual imprint of the card and put the transaction through while you wait.