The examples are shown which demonstrate that in the course of analysis of linear systems the modes with dynamic chaos can occur. This can happen when for analysis of linear systems the change of variables is used resulting in the need to investigate either non-linear equations or non-linear functions. In the plasma physics field such situation may arise, e.g., when diagnosing some plasma parameters. © 2014, National Science Center, Kharkov Institute of Physics and Technology. All rights reserved.