The following three models, which lead to the frequency independent damping, are examined: the hysteretic model, which consists of linearly elastic spring and (in parallel with the spring) Coulomb's element with the force proportional to the value of displacement; the modified hysteretic model, which is constructed by the addition (sequential) of an elastic spring to the foregoing model; the quasi hysteretic model, which has a structure similar to the hysteretic model but takes account of mean values of displacements and velocities. Some basic problems of theory of vibrations for a single-degree-of-freedom system (action of an instantaneous impulse; free vibration due to an initial non-zero displacement; response to a suddenly applied constant force; vibration under the action of periodic forces) are considered. A comparison is carried out for results corresponding to the models and also to the model with constant complex stiffness and model with viscous damping.