The cationic hydride alkylidene complexes [Tp^Me₂Ir(?CH-CH₃)(H)(PMe₃)]⁺ and [Cp*Ir(?CH-CH₃)(H)(PMe₃)]⁺ (TpMe₂ = hydrotris(3,5-dimethyl-1-pyrazolyl)borate; Cp* = pentamethylcyclopentadienyl) are experimentally known to tautomerize to the corresponding hydride alkene species. Our computational study on the mechanism shows that the reaction takes place through formation of the corresponding alkyl intermediates, with participation of species involving α- and β-CH agostic interactions. Computed energy barriers reproduce the available experimental kinetic data and agree with a much faster process in the Cp* system. The highest stabilization of the hydride alkylidene complex (the reactant) in the TpMe₂ system appears as the main reason for the higher barrier found. The difference between the two complexes is due to the steric effects of the spectator ligands.