The hydride and methyl beta-migratory insertion processes in CpM(PH3)(CH2CH2)R+ (M = Co, Rh, Ir; R = H, CH3) as well as the microscopically reverse beta-elimination reactions have been studied by relativistic density functional theory. The calculations reveal that the beta-migratory insertion reactions of the olefin hydride complexes CpM(PH3)(CH2CH2)H+ (M = Co, Rh, Ir) have electronic reaction barriers of 0.3 (Co), 2.7 (Rh), and 6.1 kcal/mol (Ir), respectively. Further, the beta-migratory insertion reactions of hydride are exothermic for cobalt (Delta H-e = -3.4 kcal/mol) and rhodium (Delta H-e = -1.0 kcal/mol), but endothermic for iridium (Delta H-e = 3.7 kcal/mol). Relativistic effects are important for the calculated trends within the cobalt triad. Without relativity the beta-migratory insertion reactions would be exothermic for all three metals. For the corresponding beta-migratory insertion reactions of methyl the barriers are 15.2 (Co), 19.8 (Rh), and 23.2 kcal/mol (Ir), respectively. The reactions are exothermic for all three metals with Delta H-e = -12.7 (Co), -8.5 (Rh), and -5.3 kcal/mol (Ir), respectively. Structures of reactants, transition states, and products were fully optimized. For the hydride migration, the transition states are close to the hydride olefin systems CpM(PH3)(CH2CH2)H+ for M = Co and Rh, whereas the transition states for the iridium hydride resemble the ethyl compound CpIr(PH3)(CH2CH2H)(+). The transition states for the methyl migration are product-like for all three metals. The most stable conformation of the ethyl and propyl product complexes CpM(PH3)(CH2-CH2R)(+) exhibits in all cases a beta-agostic M-H-C interaction. The strength of this interaction decreases down the cobalt triad. An extensive thermochemical analysis is provided for the relative stability of CpM(PH3)(CH2CH2)R+ and CpM(PH3)(CH2CH2R)(+) (M = Co, Rh, Ir; R = H, CH3).