The [CpM(PH3)H(C2H4)](+), (M = Rh, Co), complexes have been investigated with electronic structure and quantum dynamical methods. Stationary points, including transition states, have been found and characterized with various methods and basis sets. The global minimum of the Rh complex is the ethylene structure, but for the Co complex, it is the agostic structure, in agreement with experiment. A one-dimensional reaction-path profile was calculated and used for a wave packet propagation. The time-dependent wave function and the resulting spectrum have been investigated in detail. Thus, we get a first insight into the beta-hydrogen transfer process from a quantum dynamical point of view.