Hi Danan, You owe me nothing. (This is correct) For instance: "Can I pay you back for lunch?" "No, don't worry about it. You paid for my lunch yesterday, so you owe me nothing." "You didn't owe me nothing" (Incorrect) In this instance the word "anything" instead of "nothing" would be correct. For instance: "You didn't owe me anything. Why would I take your money?"

They kind of express the same meaning, but "You didn't owe me nothing," isn't a correct thing to say. It should be "You didn't owe me anything," or "You owed me nothing," because "You didn't owe me nothing," has a double negative. Also, "You owe me nothing," is in the present tense, and "You didn't owe me anything," is in the past tense. That can matter sometimes, but in general they do express similar meanings.