Many real-life applications of house allocation problems are dynamic. For example, each year college freshmen move in and seniors move out of on-campus housing. Each student stays on campus for only a few years. A student is a “newcomer” in the beginning and then becomes an “existing tenant.” Motivated by this observation, we introduce a model of house allocation with overlapping generations. In terms of a dynamic rule without monetary transfers, we examine two static rules of serial dictatorship and top trading cycles. We support these seniority-based rules in terms of their dynamic Pareto efficiency and incentive compatibility. (JEL D13, D61, D82)