We report on the first β-γ spectroscopy measurements of the neutron-rich 68–70Co and 70–74Ni nuclei, produced in proton-induced fission of 238U and ionized in a laser ion guide coupled to an on-line mass separator. Several γ lines from the decay of these nuclei have been identified, half-lives determined and production cross sections deduced. The derived level schemes for the copper and nickel isotopes show that the occupation of the ν(1g9/2) state has a strong influence on the structure of these neutron-rich nuclei. This may have a clear impact on the predicted structure and decay properties of doubly-magic 78Ni.