The approach for the determination of the theoretical strength limit in compression of viscoelastic unidirectional composite materials is proposed. The proposed approach is based on the investigation of the stability loss in the structure of the unidirectional viscoelastic composites with initial, infinitesimal local imperfections of the reinforcing layers. In this case, the corresponding investigations are carried out in the framework of the piecewise-homogeneous body model with the use of the geometrical non-linear exact equations of the viscoelastic body. As a stability loss criterion, the period of time is taken, for which the initial infinitesimal local imperfections given for the reinforcing layers start to increase and grow indefinitely. All the considered investigations are performed on the composite material consisting of the alternating layers of two materials. (C) 1999 Published by Elsevier Science Ltd. All rights reserved.