The dynamical evolution of hierarchical triple systems containing close binary systems is considered. The effects of tides on the stability of triple systems are studied, and plane triple systems with initially circular orbits for both the inner and outer binaries are investigated. The directions of revolution of both binaries are coincident; the axes of stellar rotation and the vector of the orbital angular momentum of the triple system are co-linear. Four choices for the initial rotational velocities are considered: zero velocities; synchronization of the stellar rotation with the orbital motion; average velocities for main-sequence stars of a given mass; and critical velocities corresponding to equality of the gravitational and centrifugal forces at the equators of the stars. Stars with convective envelopes are considered. It is shown that, in the case of rotational velocities that are less than the synchronized values, there is an increase in the stability of the triple system. The opposite trend is found for stars with rotational velocities that are larger than the synchronized values. The effects of tidal interactions on the stability of hierarchical triple stars could be estimated analytically using the theory of close binary systems, apart from the case of strong perturbations from the heavy distant body, and the case of small tidal effects (small eccentricities and synchronization). The equilibrium state of circularization and synchronization is not achieved in close binaries because the third body perturbs the orbit of the binary and the state of zero eccentricity is unattainable. Therefore the energy of orbital motion is continuously converted into the energies of the components.