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If your former spouse was awarded alimony (termed "spousal support" in some states) as part of your divorce, many states allow you to ask the judge to reduce or even eliminate those payments when your former spouse starts living with someone else in a marriage-like relationship. To prove cohabitation sufficient to reduce or terminate your alimony obligation, you must demonstrate not only that your former spouse and the other person are living together, but that there are economic consequences that have resulted in your former spouse not having the same financial need that they did when you divorced. [1] X Research source