Visa is the only brand of credit card that Costco accepts at this time, but they will accept any debit card.
I have used visa and amex
I know that they don't accept capital one credit card.
Well we have used our Wells Fargo credit card and debit card to make purchases.
They only accept Visa as credit but they do take all debit cards. So even if your debit card has a MasterCard logo you can still use it just can't run it as credit.
You can only use their Credit Card which I believe is thru Citi Bank now. However, you can use your bank issued card.
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