The problem of deriving reduced-order models of a higher-dimensional system from its state-space description is considered under the constraint that the model-reduction procedure should not involve the evaluation of system eigenvalues, should not involve any optimization algorthm and should yield a stable lower-order model for a stable system. The Routh-approximant modelling procedure in the frequency domain has the above characteristics. A time-domain adaptation of the Routh-approximant frequency-domain modelling procedure is presented to achieve the above objectives for s. i. s. o. systems. The lower-order time-domain model matrices are derived by a suitable truncation of the original system matrices in their gamma - delta canonic structure. The aggregation matrix relating the system and model state vectors is also derived. A numerical example is included.