Nebraska does not currently have common law marriage. There are some states that still do, and a common law marriage can exists if people held themselves out as married in one of those states.
Depending on the length of the relationship, there would need to be more research to determine if it would qualify as common law marriage in Nebraska. But no at least since 1994.
While there is no common law marriage, the court can still divide jointly owned property, provide for custody and child support.