Transmission electron microscopy (TEM) has been used to investigate the mechanisms of misfit strain relaxation in InxGa1-xAs epilayers grown on GaAs((111) over bar)B substrates misoriented 2 degrees towards [2 (1) over bar (1) over bar]. It was found that the relaxation was brought about by a triangular network of misfit dislocations lying along the three <1 (1) over bar 0> directions near the interface. However, the dislocation distribution was anisotropic with a much higher density of dislocations lying parallel to the [0 (1) over bar 1] direction. A second relaxation mechanism was also observed which involved the formation of deformation twins. These had nucleated at the epilayer surface and grown down into the epilayer, sometimes entering the underlying buffer layer. Twin formation was also anisotropic with twins forming on the ((1) over bar 11)[211] system only. The dislocation and twin anisotropy may not be explained using the Schmid Factor considerations but is thought to be associated with heterogeneous nucleation of dislocations at the [0 (1) over bar 1] surface steps caused by the misorientation. The critical layer thickness for the observation of misfit dislocations by TEM in In0.25Ga0.75As ((111) over bar)B epilayers was found to be between 15 and 25 nm. This is the same range as that observed for (001) epilayers of the same composition. This is as expected from theoretical considerations of the effects of orientation on the elastic modulus and the strain relieving component of the misfit dislocation Burgers vector. (C) 1997 American Institute of Physics.