Within the framework of the piecewise homogeneous body model with the use of the three-dimensional geometrically nonlinear exact equations of the theory of viscoelasticity the approach for the investigation of the internal stability loss (microbuckling) in the structure of the viscoelastic unidirected fibrous composites under compression along the fibers is developed in this work. This development concerns mainly the cases where the interaction between the fibers is taken into account and all investigations are carried out for the infinite viscoelastic matrix containing two neighbouring fibers. As a microbuckling criterion the initial imperfection criterion is used and co-phase microbuckling mode in plane and co-phase microbuckling mode out of plane are considered. The numerical results illustrating the influence of the interaction between the fibers on the values of the critical time are presented. (C) 2004 Elsevier Ltd. All rights reserved.