Part I: Reactions of 3-substituted 1-azabicyclo[1.1.0]butanes (1a and 1b) with dichlorocarbene proceed in each case via nitrogen ylide intermediates with concomitant ring opening to afford the corresponding dihaloimines (2a and 2b, respectively). Part II: Vinylidenecarbene-cycloalkyne equilibria have been studied in three polycarbocyclic systems, i.e., 10a-10b, 20a-20b, and 27a-27b. In all three systems, only the vinylidenecarbene intermediate can be trapped in situ by cyclohexene. The results of site-specific 13C labeling studies that employ 9-C(8)-13CBr2 (enriched with 4 atom-% 13C), 19-C(4)-13CBr2 (enriched with 5 atom-% 13C), and 23-C(4)-13CBr2 (enriched with 10 atom-% 13C) also support this conclusion and suggest that cycloalkyne intermediates, if formed in these systems, must rearrange very rapidly to the corresponding (thermodynamically favored) vinylidenecarbenes. Part III: Base-promoted reactions of N-tosyl- and N-benzhydrylazetidin-3-ones (i.e., 30a and 30b, respectively) with diethyl diazomethylphosphonate (DAMP), when performed in the presence of cyclohexene, in each case afford exclusively the product that results via in situ trapping of the corresponding vinylidenecarbene.