In this paper a numerical method for computations of electromagnetic fields is presented, which has been developed by the authors and their colleagues since 1978 under the name of the multiple multipole (MMP) method. In the meantime several groups are working independently on similar methods (with sometimes different approaches and different names). The majority of them agreed to use the name generalized multipole technique (GMT) in the future (Ludwig, 1989). The main advantages are as follows: (1) Only the boundaries of the domains have to be discretized (even in the case of lossy bodies). (2) No integrals have to be solved numerically which reduces the computation time and simplifies the codes. (3) Plotting errors on the boundaries and fields allows an excellent control of the results. (4) The fields may be computed accurately in the near-field region and even on boundaries for closed and open problems. (5) Efficient programs including graphic input and output routines (also animated pictures) are available even for personal computers.