In the season 4 episode Here Comes the Brides, Adam Simms and his son Luke move to Walnut Grove. Adam meets the school teacher Miss Eva Beadle and they marry at the end of the episode. At the same time, Luke meets Nellie Oleson and the two elope.
Luke and Nellie travel to Sleepy Eye to elope but are interrupted by both Adam Simms and Miss Beadle at the hotel in Sleepy Eye. Despite Harriet Oleson’s request that Nels makes Nellie a widow, Nellie and Luke return to the justice of the peace that married them, to undo the marriage because the pair were too young. It is after this that Adam and Eva marry by the same justice of the peace.
This is a favorite early episode of Nellie Oleson fans because it shows a kinder side to Nellie which we don’t usually see on the show until the later seasons when she marries Percival.
Luke only appeared in this single episode, so he and Nellie did not continue their relationship after they were “unmarried.”