The force between two ‘misfit’ dislocations in the interface between two crystals having lattice parameters differing by a fraction ∊ equals the force between any two dislocations having the same Burgers vectors. The misfit dislocations are driven together by the shear stress in the interface. This stress is calculated for the case of two elastic half cylinders of radius R. When the half cylinders are embedded in a medium having the same elastic constants, the shear stress in the interface at a distance × from their axis is F In [(R +x)(R−x)], where F = ∊μ/2π(l−v). When the cylindrical boundary is freed, the stress near the axis is reduced to 16FxlSR, and the stress at the edge to 2F. The equilibrium spacing of the first few misfit dislocations to enter the interface is of order (bR/∊)1/2, but the spacing approaches the final value of b/∊ when half of the interface contains misfit dislocations.