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We study the dynamics of expansion of the homogeneous isotropic Universe and the evolution of its components in the model with nonminimally coupled dynamic dark energy. Dark energy, like other components of the Universe, is described by the perfect fluid approximation with the equation of state (EoS) pde = wρde, where the EoS parameter w depends on time and is parameterized via the squared adiabatic sound speed c2 a, which is assumed to be constant. On the basis of the general covariant conservation equations for the interacting dark energy and dark matter and Einstein's equations in the Friedmann-Lemetre–Robertson-Walker metric we analyze the evolution of the energy densities of the hidden components and the dynamics of expansion of the Universe with the two types of interaction: proportional to the sum of the densities of the hidden components and proportional to their product. For the first interaction the analytical expressions for the densities of dark energy and dark matter were obtained and analyzed in detail. For the second one the evolution of densities of hidden components of the Universe was analyzed on the basis of the numerical solutions of their energy-momentum conservation equations. For certain values of the parameters of these models the energy densities of dark components become negative. So to ensure that the densities are always positive we put constraints on the interaction parameter for both models. [ABSTRACT FROM AUTHOR]