Part I of this dissertation is concerned with the problem of the magnetic field dependence of the surface impedance of superconductors, with particular reference to tin. In chapter 1 the predictions of the simple theory for the behaviour of the surface impedance for different frequencies and fieid configurations are described and compared with the results of previous experiments. Chapter 2 deals with the experimental side of the present work, where a frequency of 170 Mc/s was used, and in chapter 3 the results obtained are discussed. In chapter 4 the attempts which have been made to account theoretically for the experimental observations are reviewed. Part II of the dissertation is concerned with another problem in superconductivity, namely the behaviour of superconducting systems partitioned by thin barriers of substances which in bulk are not superconducting. The theory of such systems is developed, the consequences investigated in some detail and the present experimental situation reviewed.