Huisgen's 1,3-dipolar cycloadditions become nonconcerted when copper(l) acetylides react with azides and nitrile oxides, providing ready access to 1,4-disubstituted 1,2,3-triazoles and 3,4-disubstituted isoxazoles, respectively. The process is highly reliable and exhibits an unusually wide scope with respect to both components. Computational studies revealed a stepwise mechanism involving unprecedented metallacycle intermediates, which appear to be common for a variety of dipoles.