We calculate the damping of excitations due to four-fermionic interaction in the case of two-dimensional superconductors with nodes in the spectrum. At zero temperature and low frequencies it reveals gapless ω3 behavior at the nodal points. With the frequency increasing the crossover to the normal-state regimes appears. At high frequencies the damping strongly depends on details of a normal-state spectrum parametrization. Two important particular cases such as the models of almost free and tight-binding electrons are studied explicitly and the characteristic scales are expressed through the model-free parameters of the spectrum at the nodal points. The possibility of crossover in temperature dependence of damping in the superconducting phase is discussed.