Is it illegal for a broker to execute a market stock order not on the same day?

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For instance, 2 or 3 days later, when the price of the stock purchased is very different from what it was when I put the order to the broker?
Thanks for the answer. The market order that I had in mind is a simple market order, not a Good Till Canceled order. My father is a customer of Chase, and whenever he orders a certain amount of stocks for a given company (like Microsoft), the broker executes the order only 2-3 days later. I understand that settlement is supposed to be up to 3 days later, but not execution of the order, an I not correct? Thanks.