Fission fragments from the reaction 237Np(p ,y f) have been measured in coincidence with muonic X-rays. The efficiency of the fission fragment detector is determined from (p , 7f)-data of the same experiment. The total fission probability per p-stop Pt has been measured as well as the fission probabilities Pf of the non-radiative muonic (3d~ ls)-and (2p~ls)-transitions; the latter has been divided into two parts leading to different mean excitation energies E: Pt=(54_+17)%, Pf(3d--*ls)=(41__21)%, Pf(2p--~ls, E= 6.218 MeV) = (61 _+ 19)%, andPf(2p~ls, E = 6.525 MeV) = (57 _+ 18)%. The influence of the muon on the fission barrier is discussed. The fission probability after muon capture is compared with a calculated value using a distribution of nuclear excitation energies following muon capture and the fission probability as measured in a a38U (3He, ~f)-reaction.