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(ⁿBu)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 4.8 kcal mol⁻¹ (Δ^‡G^SD_L) 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 7.0 kcal mol⁻¹ (Δ^‡G^SD_L). These calculations are in excellent agreement with experimental findings.