In study with the help of the spectrum of maximal Lyapunov exponents, dynamic regimes of the stick-slip effect were studied with allowance effect of hereditarity. Spectrum of the Lyapunov exponents were constructed using the Wolff algorithm with Gram-Schmidt orthogonalization depending on the values of the control parametersfriction and adhesion coefficients, as well as fractional index values, which determine the heredity of the dynamical system under consideration. The existence of an area of

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... positive values of the maximum Lyapunov exponents is shown, which indicates the presence of chaotic regimes. Oscillograms and phase trajectories are constructed. Statement of the problem There are various approaches to describing the stick-slip effect, for example, taking into account the atomic structure of friction bodies [8], in [9] the study of sliding objects and structures was carried out by modifying the Newmark model -a model of a rigid sliding block with Coulomb friction. This