The damping coefficient and the length of transversal (at the frequencies from 100 to 300 Hz) and longitudinal (at the frequencies from 0.1 to 3 Hz) surface waves have been measured as a function of the concentration of solutions of poly(ethylene glycol)s (PEG) and poly(ethylene oxide) (PEO), and the molecular weight of the polymer. A local maximum of the damping coefficient of transversal waves has been discovered for dilute solutions of PEG 300. This maximum disappears and the damping coefficient decreases monotonically with the concentration of polymers of higher molecular weight in the region of dilute solutions. A fast increase of the damping with concentration has been discovered for semidilute solutions. These experimental data are used for the calculation of the real and imaginary components of the dynamic surface elasticity as a function of concentration and frequency. The obtained dependencies can be explained with the help of a dynamic model of the surface layer of polymer solutions where the main relaxation processes are connected with the monomer exchange between different regions of the surface layer. In the investigated concentration range, the corresponding relaxation time determined from the experimental data changes by more than 2 orders of magnitude.