Density functional theory calculations were performed to elucidate the mechanism of the ruthenium-catalyzed hydroamidation of terminal alkynes, a powerful and sustainable method for the stereoselective synthesis of enamides. The results provide an explanation for the puzzling experimental finding that with tri-n-butylphosphine (P(Bu)3) as the ligand, the E-configured enamides are obtained, whereas the stereoselectivity is inverted in favor of the Z-configured enamides with (dicyclohexylphosphino)methane (dcypm) ligands. Using the addition of pyrrolidinone to 1-hexyne as a model reaction, various pathways were investigated, among which a catalytic cycle turned out to be most advantageous for both ligand systems that consists of: a) oxidative addition, b) alkyne coordination, c) alkyne insertion d) vinyl-vinylidene rearrangement, e) nucleophilic transfer and finally f) reductive elimination. The stereoselectivity of the reaction is decided in the nucleophilic transfer step. For the P(Bu)3 ligand, the butyl moiety is oriented anti to the incoming 2-pyrolidinyl unit during the nucleophilic transfer step, whereas for the dcypm ligand, steric repulsion between the butyl and cyclohexyl groups turns it into a syn orientation. Overall, the formation of E-configured product is favorable by 5.0 kcal/mol (Δ‡GLS) for the catalytic cycle computed with P(Bu)3 as ancillary ligand, whereas for the catalytic cycle computed with dcypm ligands, the Z-product is favored by 5.9 kcal/mol (Δ‡GLS). These calculations are in excellent agreement with experimental findings.