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Unfortunately, under Federal law alimony is considered a non-dischargeable debt, meaning that bankruptcy will not absolve you of your requirement to pay it. Not only that but the 2005 Bankruptcy Abuse Prevention and Consumer Protection Act requires that alimony and child support payments are prioritized. That is, they must be paid off first before other creditors.
If you simply stop paying A modification of your alimony obligation can be negotiated, or your spouse can agree to delayed payments. Alternatively, your wife could simply take you to court to try to collect what you're unwiling/unable to pay. If there is a major change in your circumstances that makes you unable to pay the alimony that was negotiated at the time of your divorce -- a loss of your job, for example, or some kind of catastrophe -- then you could apply to the courts for some hardship relief to prevent the necessity of further alimony payments. But in general, in court proceedings, the court will attempt to balance who would suffer greatest, the person who has to pay the alimony or the person deprived of it, and if they find that you should be able to meet your basic living expenses and still pay alimony, you're going to be required to do so.