This paper presents the time-domain Pade approximation and modal-Pade method for single and multivariable systems. In the first part of the paper, Pade equations are derived for SISO and MIMO systems by assuming a state-space description of the higher order system and its reduced order model. For a SISO system, it is shown that these Pade equations are the same as the Pade equations obtained by a frequency-domain procedure. However, for a multivariable system, it is shown that, although a full Pade approximation exists in the frequency domain, the time-domain procedure leads only to a partial Pade approximation. In the next part, the time-domain modal-Pade method for SISO and MIMO systems is proposed. A relationship between the state vectors of the system and the model is derived for the modal-Pade reduction procedure and is referred to as an “exact aggregation matrix.”. © 1987 IEEE