Abstract <p>The character of instability development in anomalously stratified viscoelastic geosystems is studied. A new methodology for such a study is proposed, based on the results of investigation of stability and instability of elastic comparison systems, for which it has been possible to obtain both sufficient stability conditions and sufficient instability conditions in couple with the character of instability development. It is clarified that the corresponding viscoelastic system (with regard for previously substantiated choice of viscoelasticity models of an adequate type) is unstable both in the case of stability and in the case of instability of the elastic comparison system, however, the character of instability manifestation in these two cases is completely different. In the case of instability of the elastic comparison system, the instability of the investigated viscoelastic system develops dynamically, and the rate of its development exceeds estimated in the work the rate of instability development of the elastic comparison system, which provides a lower bound for the sought rate. In the case of stability of the elastic comparison system, the development of instability of the viscoelastic system proceeds slowly (and the slower the greater the viscosity). In this case, the rate of instability development in a viscoelastic system somewhat exceeds the rate of instability development in a viscous fluid with the same viscosity and the same anomalous stratification, which again provides a lower bound for the sought rate. The proposed method is a convenient and effective tool for studying the character and rate of instability development in viscoelastic geosystems.</p>