Some processes such as fractional order processes cannot be represented by state space equations. Large dimensional multi-input multi-output processes with time delays have approximated state space representations, but the number of state equations can be too large to handle. For such processes, fast Fourier transformation (FFT) methods can be used to simulate them. However, when the frequency responses and time responses have long tails, the FFT methods suffer from long computation time because they require a large number of frequency response data points. Both cases experience reduced efficiency for the FFT-based simulation methods. Here, a method based on series and/or parallel compensations is proposed to solve these problems. Simulation results for various processes including transcendental processes and large dimensional processes with time delays show that the proposed method is promising and can be used advantageously, complementing the state space method. (C) 2003 Elsevier Ltd. All rights reserved.