In 1224 Hallveig Ormsdottir, who was at the time the richest woman in Iceland, moved to live with Snorri at Reykholt. She was a lot younger then him and had two sons from her previous marriage, but she had been married to Bjoern Thorvaldsson at Hruni, who had been killed. It's not considered likely that Snorri and Hallveig ever got married and people have speculated if Snorri and Herdis ever got legally divorced. Though most people think that Snorri's and Hallveig's relationship was for their personal gain, the fact was that their relationship was quite tight and full of love and it seems that they were very dear to each other, because Snorri was absolutely heartbroken when he heard of her death.
In spite of all of this, Snorri and Hallveig never had any children together but Hallveig's two sons grew up with them at Reykholt. Snorri had two children with Herdis, Hallbera and Jon murtur. Then again Snorri had children with three other women, one child per woman who all seem to be born the next few years after Snorri left Borg a Myrar. The oldest of those three children was Ingibjoerg but her mother's name was Gudrun, the daughter of Hreinn Hermundarson. Gudrun had more children with Snorri but Ingibjoerg was the only one who grew up to bee an adult. The second child was a girl called Thordis but her mother's name was Oddny, and that's about everything yet known about those two. Finally Snorri had a son with Thuridur, the daughter of Hallur Oraekjuson. This son's name was Oraekja.