Roland: ... is actually not as easy as it sounds! It was really about time to cancel our Costco membership as it does cost quite a buck every year which may be ok when you regularly buy there, but does not make that much sense when you live in a country where they do not have a Costco (as unbelievable as that may sound to our North American readers).
So step 1 would be to cancel the Amex card that is associated with our account. The obvious first idea was to call the customer service number that is printed in microscopic letters on the back of the card. As expected I was connected to a computer voice that asked me for my card number and password. Once I had done that it gave me the choice to access any possible information regarding my account, but it did not give me an option to talk to a live operator. So I checked the net for alternative numbers, found a few of them, tried them all, and ended up with the same result as the first time. Then I lied to the computer stating that I did not have my credit card available (although I did not want to report it as stolen) planning on being connected to a human being, but no... it asked for my name, date of birth and social security number to access my account and give me the usual information once again.
A bit frustrated I called a GERMAN Amex number I found on the net. I was connected to the usual computer voice (obviously in German this time) that actually offered my one more choice: hit # for operator! The operator was Ines, a very nice Lady, who could not help me with my inquiry, but who connected me to the American branch of Amex, where I talked to Jonah, who could not help me either, but who connected me to the Canadian branch of Amex, where I talked to Virginia, who could not help me (other than changing our address on the account), but who connected me to Frank, who had our account closed within a minute.
And by the way, I was told to just hit the # key after calling the service number on my card to speak to an operator. Could they not have the computer tell you that when you call?! Anyway, the account is closed now, next step is to close the Costco membership. This time I will use email!