The quantum dynamics of beta-hydrogen elimination in cationic transition metal complexes [CpML(C2H4)H](+) (M = Co, Rh; L = PH3, PF3, PMe3, P(OMe)(3)) is studied theoretically. The underlying potential energy profiles are obtained at the DFT level of theory; the nuclear motion is computed by the method of wave packet propagation (i.e., by integrating the time-dependent Schrodinger equation). For the Co as well as the Rh complexes, agostic intermediates relevant to the insertion/elimination process exist. Complexes containing each ligand are studied for both transition metals from an electronic structure point of view and, in addition, the ligand influence on the dynamics is compared. The results allow us to draw conclusions concerning the influence of the energetics as well as the different masses on vibrational periods and lifetimes of these complexes due to beta-elimination.