Strained cyclic allenes are short-lived intermediates that confine a functional group with a preferred linear geometry, an allene, into a small ring, inducing strain-driven reactivity. Nitrogen-containing variants, or azacyclic allenes, have proved valuable for the assembly of complex nitrogen-containing compounds. Whereas 3,4-azacyclic allenes, which bear a symmetrical core, have been the focus of multiple studies, their unsymmetrical 2,3-azacyclic counterparts have remained underexplored. In the present study, we report density functional theory studies investigating the structure of such unsymmetrical azacyclic allenes and experimental efforts to access and engage them in strain-promoted cycloadditions under mild conditions. Control experiments support either concerted or stepwise diradical mechanisms for these reactions, depending on the type of cycloaddition examined. Moreover, we generate the corresponding 2,3-oxacyclic allene and demonstrate its reactivity in cycloadditions and a metal-catalysed process. Given the scaffolds accessed, coupled with the observed selectivity trends, these results are expected to encourage the application of unsymmetrical heterocyclic allenes for the synthesis of heterocycles that bear a high fraction of sp3-hybridized atoms.