The complex dynamic elasticity of monolayers of the diblock copolymer poly(styrene)-poly(ethylene oxide) at the air-water interface in the pancake, quasi-brush, and brush regimes has been studied by means of three experimental techniques - the surface transverse and longitudinal waves and the oscillating barrier method. In the pancake regime the surface viscoelastic properties in the frequency range under investigation (0.01-520 Hz) prove to be indistinguishable from the surface properties of the homopolymer PEO. Transition to the quasi-brush regime is accompanied by rather abrupt changes in both components of the surface viscoelasticity. The surface viscosity in the brush regime exceeds significantly the results calculated from the theory of D. M. A. Buzza et al. (J. Chem. Phys. 109, 5008 (1998)), which takes into account the dissipation arising from the flow of solvent through the brush phase. Possible reasons of this discrepancy are discussed.