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You go to your nearest LDS Family History Center and ask them to help you find out if the marriage records for that time period have been microfilmed. If they have, you pay about $3 to have the film sent there so you can spend hours with your head stuck in the hood of a microfilm reader until you hit paydirt. If you haven't searched microfilm before, keep a wastebasket nearby. It takes some people a while to get over the vertigo from watching the pages slide past.
Two other alternatives are a local historical society and the courthouse. Apparently the local community college has a collection in its library, because it is listed in Everton's Handbook under Genealogical Archives, Libraries and Societies. East Arkansas Community College, Forrest City, AR 72335-9598.
The County Clerks office has marriage records from 1875, probate records from 1910 & tax records. Saint Francis County, 313 S. Izard St., Forrest Ciry, AR 72335-3856. You may have to pay a local genealogist to go to the courthouse and search for you if you don't have a definate date. I'd start with the Community College, then the LDS, and Court House last. Courthouse employees are there to take care of "todays" business and many have been turned off by genealogists who expect them to do our work for us, you may not get a good reception there. Sure wouldn't hurt to give them a call and ask what their policy is. Good luck.