Are you sure he is telling the truth?
Have your items ended?
Were they auction items and had the full seven days elapsed?
Are the items in your Unsold Items list?
Are the items still active?
Is there any indication of the sale in your Paypal account?
Have you closed your computer, had a nice walk around the block and come back to find the same problem?
If the item has closed, but the customer was not billed by eBay, he may be trying to buy off-eBay after the listing ended.
You can bill him through Paypal's Send Money, adjusting the shipping as necessary for the multiple purchase, and give the eBay listing numbers in the textbox.
Or you can Block the bidder from the Site Map-> Manage Bidders.