Abstract: High-spin states of K-40 have been populated in the fusion-evaporation reaction C-12(Si-30,np)K-40 and studied by means of gamma-ray spectroscopy techniques using one triple-cluster detector of the Advanced Gamma Tracking Array at the Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Legnaro. Several states with excitation energy up to 8 MeV and spin up to 10(-) have been discovered. These states are discussed in terms of J = 3 and T = 0 neutron-proton hole pairs. Shell-model calculations in a large model space have shown good agreement with the experimental data for most of the energy levels. The evolution of the structure of this nucleus is here studied as a function of excitation energy and angular momentum.