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In this paper there are presented methods of study for the automatic regulation of the absolute stability in case of the nonlinear dynamical systems. There are specified two methods for the absolute stability with criteria and mode of application: a) the Lurie method with the effective determination of the Liapunov function; b) the frequencies method of the Romanian researcher V. M. Popov using the transfer function for the critical cases. The nonlinear dynamical systems which include nonlinear and linear blocks are reported to the special classes. Due to the coposed perturbations with inverse response action of the automatic regulator components these will lead to obtaining an absolute stable regime. The mathematical modelling is numerically analysed, and the realized application by these two methods is used in the metal cutting tools machine, in the absolute stability of the rate of aircrafts equipped with autopilot or in the case of the rolling oscillations for the ships.