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Credit card companies usually provide their terms in the credit card application/offer, and that would be your written agreement with them. The credit card terms are drafted by the credit card companies, and they will not negotiate them with you, so I suppose in that sense they are adhesion contracts (i.e., a borrower needs to adhere to those terms or no contract is formed). However, given the amount of regulations in that industry, I do not believe a borrower these days can be relieved of paying credit card debts by alleging they are adhesion contracts. Be sure to consult your own attorney to protect your legal rights.
Contracts of adhesion are basically take it or leave it agreements. Since your credit card is issued with an agreement to which you did absolutely no negotiation, then yes, technically, credit cards are adhesion contracts.
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You _DO_ have a written contract -- you just misplaced it. You signed or clicked through part of the agreement. You also received a printed copy of the terms of the agreement about the time the card was issues. You have been receiving bill-stuffer amendments to the agreement right along. All of these things together define the agreement.
But, yes, it's a contract of adhesion because you had no meaningful opportunity to negotiate any of the terms.