2-Ethoxy- and 2-(ethylthio)-1-azetines readily undergo 1,3-dipolar cycloadditions with nitrile oxides and nitrile ylides to give stable 4,5-bicyclic cycloadducts. With nitrilimines, however, the expected 1,3-dipolar cycloadducts and/or unexpected ring-opened products, namely 1,2,4-triazoles, are formed depending on the nature of the nitrilimine N-substituent. In contrast, the azetines fail to react with nitrile sulphides, azomethine ylides, nitrones, aryl azides, and various dienes. X-ray crystallographic data on the nitrile oxide, nitrile ylide, and nitrilimine cycloadducts, and on the 1,2,4-triazoles, are presented. Also a mechanistic rationale for triazole formation is offered.