This thesis presents a study of InGaAs epitaxial layers grown on vicinal GaAs.In particular it investigates the surface morphology of such layers with the use of Atomic Force Microscopy, Nomarski Differential Interference Microscopy and the relation of this morphology to the misfit dislocation array on the interface. The I would like to thank my supervisor Peter J. Goodhew for his encouragement and support throughout this project. Also, Dr Robert Murray for his valued criticism of this manuscript and invaluable hours of discussion upon a variety of topics. I am also indebted to Dr Tim B. Joyce for the CBE growth of my samples and Guy Cohen (Technion, Israel Institute of Technology) for the DCXRD measurements The help of all those in the Department of Materials Science and Engineering and the CBE group of the University of Liverpool should also be acknowledged and especially Georgios Petkos and Dr Glyn Macpherson. I could not have had better financial support than that given by the European Commission under the Training and Mobility of Researchers Programme. I would also like to thank Pat Owen for her generous help from the first moment that I came to Liverpool and my friend Fedon Antonakopoulos for making my stay more enjoyable. The support of my colleagues, Dr Adam Boyd, Sue Sajip, and Muhammad Azmi Abdul Hamid has also been very important for the completion of this work. Finally, I am grateful to my family for supporting me throughout my studies."Strain Relaxation In III-V Semiconductor Heterostructures ", P. J. Goodhew and K.