This paper presents a corpus and experiments to mine possession relations from text. Specifically, we target alienable and control possessions and assign temporal anchors indicating when a possession relation holds between the possessor and possessee. We work with intra-sentential possessor and possessees that satisfy lexical and syntactic constraints. We experiment with traditional classifiers and neural networks to automate the task. In addition, we analyze the factors that help to determine possession existence and possession type and common errors made by the best performing classifiers. Experimental results show that determining possession existence relies on the entire sentence, whereas determining possession type primarily relies on the verb, possessor and possessee.