The uncertain origin of the proton rich Mo and Ru isotopes has motivated cross-section measurements of alpha- and neutron-induced reactions. The experiments were performed via the activation technique by irradiating thin layers of natural ruthenium with alpha-particle beams close to the Gamov window of the p process between 7.0 and 10.5 MeV. The cross sections of the reactions Ru-96(alpha,gamma), Ru-96(alpha,n), Ru-96(alpha,p), and Ru-98(alpha,n) could be determined with uncertainties of typically 10 about two to three times smaller than recent statistical model predictions. Additional activations in a quasistellar neutron spectrum corresponding to kT=25 keV allowed us to obtain the complementary stellar (n,gamma) cross sections for Ru-96, Ru-102, and Ru-104. In these cases the agreement with model calculations is considerably better.