Consider a T-period, bilateral matching economy without monetary transfers. Under natural restrictions on agents’ preferences, which accommodate switching costs, status-quo bias, and other forms of inter-temporal complementarity, dynamically-stable matchings exist. Generally, “optimal” dynamically-stable matchings may not exist, but under a suitable partial order the stable set forms a lattice. The welfare properties of different stable outcomes is ascertained and the implications for normative market- design are discussed. The robustness of dynamically-stable matchings with respect to the market’s time horizon is examined.