This paper studies investment incentives in the steady state of a dynamic bilateral matching market. Because of search frictions, both parties in a match are partially locked-in when they bargain over the joint surplus from their sunk investments. The associated holdup problem depends on market conditions and is more important for the long side of the market. In the case of investments in homogenous capital only the agents on the short side acquire ownership of capital. There is always underinvestment on both sides of the market. But when market frictions become negligible, the equilibrium investment levels tend towards the first-best.