Investigations of viscoelastic composite materials and structural members carried out using the TDLTSDB and initial-imperfection method are reviewed. The investigations address the internal and surface loss of stability of layered and fibrous composites, the loss of stability of plates, and the delamination (buckling) of plates with cracks. Each of these problems is reviewed separately. New areas of further research are proposed. The review focuses on the investigations carried out by the author and his students.