The mechanism and chemoselectivity in the cycloaddition of ynamides and isoxazoles have been explored by the density functional theory (DFT) in model systems composed of a Brønsted acid (HNTf2), gold(i) [IPrAuNTf2] or platinum(ii) (PtCl2/CO) catalyst, either with or without the presence of H2O. The DFT calculations reveal that all these catalysts entail similar nucleophilic attack of isoxazole on the catalyst-ligated ynamide forming a vinyl intermediate, which can isomerize to an α-imino intermediate upon cleavage of the isoxazole N-O bond. The completely distinct reaction pathways are observed after the formation of the α-imino intermediate. For the Brønsted acid catalyst, [5 + 2 + 1] cycloaddition with H2O is the favorable way to generate O-bridged tetrahydro-1,4-oxazepines. If the Brønsted acid is replaced by a gold(i) catalyst, a [3 + 2] cycloaddition product is produced, either in the absence or in the presence of H2O. Regarding the Pt(ii) catalyst, 1,3-oxazepines are formed through [5 + 2] annulation. Furthermore, the [5 + 2] annulation product in this Pt(ii)-catalyzed system can also be predicted upon addition of H2O. The unique properties of the three selected catalysts were explored in detail through distortion/interaction analysis. The obtained theoretical data account for an observed disparate product formation when using three catalytic systems and provide a theoretical foundation to choose the optimal catalyst for the title reaction. These results can be of particular significance for synthetic chemists toward the design of catalytic systems and cycloaddition transformations involving ynamides, isoxazoles and related derivatives. This journal is © The Royal Society of Chemistry.