A combined magnetic round lens and deflection system with a superimposed field has been studied, and the power series expressions for the magnetic field is given. The electron trajectories are described in vector-form, and the Gaussian optical properties of the combined system discussed. By means of Fermat's principle general aberration formulae for the combined system have been derived. Equations for calculating the third-order aberration are given in compact matrix-form, hence they are suitable for numerical computation. This paper attempts to give a general theory of the combined system to provide guidance for designers of cathode ray tubes and electron optical instruments.