Surface quasi-elastic light scattering (SQELS) has been used to obtain the temporal evolution of capillary waves when graft copolymers of polymethyl methacrylate and poly(ethylene oxide) have been spread as monolayers at the air-water interface. The graft copolymers had a polymethyl methacrylate backbone and poly(ethylene oxide) grafts, containing 54 ethylene oxide units. The capillary wave frequency had a maximum at a surface concentration which is unique for each copolymer. At this same concentration the capillary wave damping shows a sharp 3- to 4-fold increase. Graft copolymer composition is the factor determining the surface concentration at which this frequency maximum and increase in damping are observed. Modeling the transverse surface viscoelastic properties as a Maxwell fluid shows that there is a distinctive change in the relaxation time of this mode at this surface concentration. A phase transition takes place, the poly(ethylene oxide) grafts becoming immersed in the subphase to a significant extent at this point. Dilational moduli obtained from the surface quasi-elastic light scattering exhibit the features of an absorption resonance, and the dilational viscosity has a divergence at this unique surface concentration. These last two surface viscoelastic parameters show behavior akin to that described by Kramers-Kronig relations but they are unique in that they can only be modeled by invoking a resonance with the velocity component of an applied oscillatory force. Negative dilational viscosities have been obtained, a finding which has been interpreted as energy transfer to the dilational mode from some other source. Reasons for this observation are considered but no definitive source of the additional energy contribution has been identified and the possibility that the dilational viscosity is an effective parameter is discussed together with a consideration of other contributions to the dispersion equation of the surface modes.