Dedicated to Professor Wolfgang Sprößig on occasion of his 70th birthday.Abstract. This paper presents an operational framework for the computation of the discretized solutions for relativistic equations of Klein-Gordon and Dirac type. The proposed method relies on the construction of an evolutiontype operador from the knowledge of the Exponential Generating Function (EGF), carrying a degree lowering operator Lt = L(∂t). We also use certain operational properties of the discrete Fourier transform over the n−dimensional Brioullin zone Q h = − π h , π h n -a toroidal Fourier transform in disguise -to describe the discrete counterparts of the continuum wave propagators,∆ − m 2 respectively, as discrete convolution operators. In this way, a huge class of discretized time-evolution problems of differential-difference and difference-difference type may be studied in the spirit of hypercomplex variables.