You have to follow exactly the letter of your contract when you terminate your membership, or it doesn't count. Usually they require all communications to be in writing. You should send everything via certified mail, return receipt requested. Keep the receipts forever. Otherwise, if this were to go to court, you'd have no way to legally prove you ever sent them any letters.
If you no longer have a copy of that contract, you can get it from the health club - go to the local gym in person and deliver them a written request for a copy of our contract; AND mail the health club's national office a certified letter (return receipt requested) asking for a copy of your membership contract. In those letters, be friendly and polite and don't say anything about disputing a membership - just say you lost your copy of the contract and nicely ask if you can please have another copy. Certified mail, return receipt.
Follow the membership termination process as it is spelled out in your contract. Get copies of all your credit reports, and make sure they haven't already dinged your credit. Follow up in writing with the credit reporting agencies if the health club already has done that.
If the health club keeps after you, complain to your state's "secretary of state" and "state attorney general" offices.