The vibrational spectra of linear BC3 and linear B2C2 in an argon matrix at 10 K have been observed for the first time by Fourier transform infrared spectroscopy. Mixtures of boron and carbon powders were vaporized in a resistively heated (similar to 3000 K) oven. BC3 was produced during codeposition of the vapors with argon onto a CsI substrate maintained at 10 K; B2C2 was observed only after annealing the matrices. Frequencies measured at 2002.1 and 1512.5 cm(-1) have been assigned to the nu(1)(sigma) and nu(2)(sigma) B-C stretching fundamentals of linear BC3 and a frequency measured at 955.0 cm(-1) has been assigned to the nu(3)(sigma(u)) stretching fundamental of linear symmetric BC2B. These assignments are based on FTIR measurements of the majority of the BC3 and B2C2 isotopomer frequencies and are consistent with the results from Rittby's collaborative ab initio study.