The mass surface of nuclei close to the doubly magic nuclide ⁷⁸Ni is calculated by two methods. The first relies on the multiparticle shell model based on an effective interaction and a mean nuclear potential. The second employs the concept of so-called "magic crosses" and enables us to determine the masses of odd-odd nuclei close to ⁷⁸Ni by using similarity of the shell structure and neutron-proton interaction in the region of nuclei under consideration and in the region of heavy magic nuclides. The energies of the separation of one and two neutrons from nuclei close to ⁷⁸Ni and the energies of the β decay of these nuclei - recall that these quantities of astrophysical interest - are presented.