The equilibrium configurations of monolayer films on crystalline substrates have been investigated using molecular dynamics techniques. Misfit dislocation densities are found to differ from those predicted by elasticity theory, because of the more realistic interatomic potential employed in the simulations (Lennard-Jones), and the absence of constraints on atomic positions. Two distinct dislocation core structures are observed, with a discontinuous transition between the two as the external conditions are changed. Shockley partial dislocations are found to be stable for a large range of misfits in the case of FCC (001) substrates, and recently an experimental observation of these dislocations was reported. The stability of monolayer films relative to the formation of three-dimensional clusters is also considered.