Hydrogenation of niobium cluster cations Nb-n(+) (n=2-15) in a seeded supersonic jet of H-2/He and multiple-collision-induced dissociation (MCID) of the resulting NbnHm+ hydrides have been studied using a Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer. The nascent NbnHm+ hydrides trapped in the FT-ICR cell have broad m distributions with no apparent prevalence of odd or even m. A pulse of argon applied to the trapped clusters causes a dramatic squeezing of the initial m distribution (through the collision-induced removal of weakly bound H-2 molecules), favoring several particular hydrides for each cluster size n, e.g., Nb7H8+, Nb7H11+, and Nb7H12+ for n=7. The maximum m values of these stable hydrides are close to the stoichiometric composition of NbH2 for the clusters with n < 13, and approach that of NbH at larger n. The hydrides observed in our experiments are different from the products of the Nb-n(+)+H-2 reactions performed in the FT-ICR cell at room temperature, which show only even and strongly n-dependent m values. The MCID of the NbnHm+ clusters occurs through the sequential desorption of H-2 molecules yielding NbnH+ and Nb-n(+) as final dissociation products for odd and even m, respectively. Based on the experiments on the MCID of Nb12H18+, an explanation is suggested for different reactivities of the Nb-12(+) clusters toward H-2 in the ICR and fast-flow-reactor experiments.