If you find yourself in the position that your ex is accusing you of infidelity after a divorce is final, it is understandable that you will be confused. After all, if no such concerns came up while you were married or while you were in the process of separating, it is understandable that you would be surprised that these accusations are flung your way now. Take a step back and understand that several likely reasons exist why your ex-husband might now be accusing you of having been unfaithful during the marriage.
Look at the situation you and your ex are in now and ask yourself if he would have any leverage to gain by accusing you of cheating -- even if he himself doesn't actually believe it. If you have mutual friends and acquaintances, he may want to gain their sympathy while making you look bad. If he has a tendency to act in particularly toxic ways, he might be trying to turn your kids against you. If accusing you of having cheated on him while you were married were to give him a legal advantage with issues like child custody, this could also be a reason for his accusations. This motivation is especially likely if he seems more interested in spreading rumors rather than in resolving painful issues from the past.
Making You the “Loser”
Some people feel a strong need to define breakups and divorces in terms of a winner and a loser. In other words, they want to establish that one of you is a winner, or a superior human being who is better off without the inferior loser. If your ex didn't want the divorce or is worried that he might be the loser in your marriage, it may be easier for him to believe that you cheated so that he can see you as the bad guy.
Someone Stole Your Heart
It is possible that your husband is subconsciously choosing to believe that you cheated because he wants to think that it is the reason you left. It may be less painful for him to believe that you chose another man, or even that another man convinced you to divorce him, than to face the idea that you freely chose to be single rather than stay married to him.
Of course, it is also possible that your husband is accusing you of cheating because he genuinely thinks that is what happened. If so, the reason might be some subconscious motivation like the ones above, or some new information may have become known that he has interpreted as a sign of past infidelity. He may have a friend who believes you cheated and has been able to convince him of such. In this case, look for any potential "bad influences" in his social circle or any circumstantial evidence that may have come to light, or probe your ex about both of these.
Confronting the Problem
In some cases, your ex's accusations are something you will need to deal with. If he is spreading rumors that directly affect you and your family, try talking to your friends and associates about what you think is going on. Be calm and let them know that you believe your ex is spreading these accusations to discredit you. The more confident you are when you discuss this, the better you will be able to defuse the problem. If you believe his accusation is the result of arguments or evidence presented to him by a particular friend, it may be worthwhile to speak to that person or to your ex about why that advice is not to be trusted. Bear in mind, however, that in some cases, it may be more hassle and headache than it is worth to try to change your ex's mind -- especially if his newfound belief in your infidelity affects nobody but him.