We report the first gas-phase vibrational spectra of the hydrocarbon ions C3H+ and C3H2+. The ions were produced by electron impact ionization of allene. Vibrational spectra of the mass-selected ions tagged with Ne were recorded using infrared predissociation spectroscopy in a cryogenic ion trap instrument using the intense and widely tunable radiation of a free electron laser. Comparison of high-level quantum chemical calculations and resonant depletion measurements revealed that the C3H+ ion is exclusively formed in its most stable linear isomeric form, whereas two isomers were observed for C3H2+. Bands of the energetically favored cyclic c-C3H2+ are in excellent agreement with calculated anharmonic frequencies, whereas for the linear open-shell HCCCH+ (2Πg) a detailed theoretical description of the spectrum remains challenging because of Renner-Teller and spin-orbit interactions. Good agreement between theory and experiment, however, is observed for the frequencies of the stretching modes for which an anharmonic treatment was possible. In the case of linear l-C3H+, small but non-negligible effects of the attached Ne on the ion fundamental band positions and the overall spectrum were found.