Abstract: Excited states up to J(pi) = 11(-) at 10 296 keV and J(pi) = 10(+) at 10 707 keV have been populated in the odd-odd Cl-36 nucleus using the Mg-24(N-14,2p) fusion-evaporation reaction at E-lab = 31 MeV. Twenty new states and 62 new gamma transitions have been identified by employing gamma-gamma and gamma-gamma-gamma coincidences. Lifetimes have been investigated by the Doppler shift attenuation method. The experimental data have been compared with the results of large-scale shell-model calculations performed using different effective interactions and model spaces allowing particle-hole excitations across the N = Z = 20 shell gap.