We report the complete characterization of the hot band (v(3) + 2v(5)) - 2v(5) for linear C-4 and the analogous band (v(3) + 2v(7)) - 2v(7) for linear C-5 via gas phase, rotationally resolved spectra. C-4 and C-5 were generated using a flowing mixture of acetylene and helium subjected to a hollow cathode discharge. The spectra were recorded using a diode laser spectrometer. Sigma-Sigma and Delta-Delta transitions were observed for both molecular species. Analyses of these hot bands yielded the following lower state molecular parameters: v(0) = 1547.3164(5) cm(-1), B = 5024.92(18) MHz, D = 0.924(52) kHz, X-L = 0.5802(92) cm(-1) and q(5) = 10.8890(26) MHz for C-4 and v(0) = 2166.2331(3) cm(-1), B = 2576.524(87) MHz,. D = 0.143(13) kHz, X-L = 0.409(10) cm(-1) and q(7) = 3.9845(15) MHz for C-5. The results were completely consistent with linear structures and support our previous conclusions with regard to semi-rigid linear nature of these two molecular species. This work represents the first conclusive study of a vibrational state with two quanta in the bend for any carbon cluster with four or more atoms. (C) 2004 Elsevier B.V. All rights reserved.