Measurements are reporled on polarized-proton scattering from the even-mass zinc isotopes at 20.4MeV beam energy. The elastic and first-order inelastic processes are represented well by standard theory. The analysis of the two-phonon multiplets presents difficulties which may indicate a change in the nuclear structure between isotopes or the occurrence of an energy-dependent interfering process.NUCLEAR REACTIONS 64,66.68,mZn (polarized p,p') E = 20.4MeV; measured o(e), A(0); deduced optical model parameters, deformation strengths for 2 : and 3; states. DWBA calculations;for -Zn and "Zn also cc.