Using activation techniques, the excitation functions for the 58Ni(n,2n)57Ni and 58Ni(n,np + pn + d)57Co reactions were measured in the neutron energy range from 12.7 MeV, close to the (n,2n) threshold, to 19.6 MeV with an accuracy of typically ∼4.5 and ∼6%, respectively. In the 13.4- to 14.8-MeV energy range, the accuracy achieved for the cross sections of the above reactions was typically 2 and 3%, respectively. In addition, cross sections were measured for the 58Ni(n,p)58Co reaction in the 14-MeV region with an accuracy of typically ∼2%. The experimental results were compared with calculations based on the optical model, the compound nucleus model, and the exciton model of nuclear reactions. A quite satisfactory simultaneous reproduction of all experimental data, including the proton- and alpha-production spectrum, was achieved employing a unique set of model parameters. Moreover, the new (n,2n) cross sections provide an improved data base for reactor dosimetry and spectrum unfolding applications.