In family law circles, "cohabitation" refers to a couple living together in a romantic relationship like a husband and wife would but not actually getting married. In the aftermath of a divorce, the companionship and economic contribution of a live-in significant other can be welcome. If you're receiving alimony, however, moving in with your boyfriend or girlfriend can give your ex an opportunity to stop the check.
What It Means to Cohabit
Almost everything in family law is governed by state law, so the exact definition of "cohabitation" in your jurisdiction might be considerably different from the law in the next state over. In general, however, "cohabitation" implies not only sharing an address, but also voluntarily assuming the rights and duties typically shared by a married couple. These duties include supporting each other, so courts generally consider it unfair to make an ex-spouse pay support to someone who is using it to help defray the living expenses of a new love.
While whether a given couple is cohabiting involves an analysis of the totality of the circumstances, the most important element in cohabitation is actually living together. For some couples, this can be a blurry concept; a pair might start out their relationship living in separate residences but spend more and more time together as the relationship progresses. If your significant other keeps clothes and personal items at your residence, eats there, relaxes there, sleeps there and helps you out around with the bills and chores, you may actually be cohabiting and endangering your alimony award. Just because one of you receives mail somewhere else won't necessarily protect you.
The person trying to cut off an alimony award bears the burden of proof to the court that a couple is living together and not just spending the night. Exactly how high this burden is will vary from state to state, but in civil court -- where family law cases are heard -- the burden is typically lower than the reasonable doubt standard in criminal cases. Just getting a private investigator won't necessarily make your case unless you can afford to pay the investigator to watch your ex's residence every night for weeks on end. Other proof of cohabitation can include admissions by your ex or the significant other, where she has their mail sent and what her bank records say she's paying for.
Spending the Night
Simply spending the night together on a regular basis will not suffice to cut off an alimony award. If you're not living with your significant other, each one of you has a separate address -- even if you don't spend every night there. While you may have clothes, a toothbrush and maybe even some furniture items at the other person's house, you have the same things at another one. You may prefer to spend the night together, but you haven't yet made that critical step of giving up your separate home. Be careful, though; it might not cut off your alimony award, but it can endanger it.