The (α,α′) reaction, at Eα=31 MeV, on Zn68 and Zn70 was studied with an over-all energy resolution of 70-120 keV. Angular distributions are presented. New 3-, 4+, and 5- assignments are made on the basis of distorted-wave Born-approximation (DWBA) calculations. Good angular distributions were obtained for double-excitation 2+ states at 1.88 MeV in Zn68 and at 1.78 MeV in Zn70. Fractionation of the octupole strength has been observed. Systematics of excitation energies and strengths are discussed for Zn64, Zn66, Zn68, and Zn70.