When a Ne:allene or a Ne:propyne sample was codeposited at approximately 5 K with a sample of pure neon that had been excited in a microwave discharge to provide a 16.6-16.85 eV energy source, prominent new infrared absorptions which can be assigned to the H2CCCH2+ cation appeared. Also present in the allene experiments were two absorptions which can be assigned to H2CCCH-. In the propyne experiments, an absorption is tentatively attributed to the strongest infrared fundamental of CH3CCH+. The structures and vibrational fundamentals obtained from density functional and ab initio calculations for various isotopomers of H2CCCH2+, CH3CCH+, cyc-C3H3+, H2CCCH+, and H2CCCH- are given. The infrared absorption pattern of the cation common to the allene and propyne experiments matches that of the predominant gas-phase product, cyc-C3H3+, reasonably well, except for the presence of extra peaks in the CH-stretching region. However, comparison of the results of experiments on isotopically substituted samples with the calculated spectra excludes that assignment and supports the identification of the neon-matrix product as H2CCCH2+. It is suggested that collisions with the excess of neon atoms in the sampling region rapidly remove excess energy from the initially formed allene and propyne cations, inhibiting the loss of an H atom from those two species.