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The radical cations of acetylenic hydrocarbons are important intermediates in many kinds of processes ranging from organic synthesis to interstellar chemistry. In this work we report an experimental and computational study on structure and reactivity of cyclopropylacetylene (CyPA) radical cation generated by X-ray irradiation in low-temperature matrices. The primary radical cation of CyPA was found to give an isotropic EPR signal represented six well-defined lines in Freon matrices at 77 K, in agreement with the quantum-chemical calculations. The assignment is confirmed by the effect of deuteration on the EPR spectrum. The isolated ground-state radical cation was found to be quite stable over the whole temperature range studied (up to 150 K). Photolysis of the primary CyPA radical cation with visible light (wave-length > 440 nm) results in dramatic spectral change, which was attributed to cyclopropyl ring opening. Computational analysis of six possible structures, which involve ring cleavage, reveals that (Z)-pent-3-en-1-yne radical cation is the most favorable one. In the case of CF2ClCFCl2 matrix, annealing the sample at 135K results in conversion of the primary radical cation of CyPA into a propargyl-type radical due to ion-molecule reaction of proton transfer occurring upon matrix softening (this process is concentration-dependent). The EPR spectrum of the primary CyPA radical cation (poorly resolved) was also obtained in a xenon matrix at 7 K. An attempt was made to characterize the corresponding species by FTIR spectroscopy.