Since you are the person paying the alimony, the only possible ramifications would come because of an increased ability to pay support (whether you cohabit or remarry). However, the only time that becomes important is if your ex-husband tries to modify spousal support upward - something that is very difficult to do. So, the answer is that it is more than likely that neither cohabitation or marriage is going to alter your spousal support.
Alimony is subject to modification and/or termination when the payee is cohabiting with an unrelated third party. The living arrangements of the payor does not likely affect the alimony payments. See the attached article for additional information pertaining to modification and termination of alimony: http://www.weinbergerlawgroup.com/divorce-legal-separation/post-divorce-issues/alimony-modifications.aspx
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