Following the laboratory detection by Fourier transform microwave spectroscopy of the four new methylcyanopolyynes described in the accompanying paper by W. Chenet al. (J. Mol. Spectrosc.1998), we detected two new methylpolyynes, CH3(C≡C)4H and CH3(C≡C)5H. The strongest lines of both molecules, obtained in a discharge with a dilute mixture of methylacetylene and diacetylene in neon, were quite intense: after 4 min of integration, a signal to noise of about 300 for the strongest lines of CH3(C≡C)4H and 30 for those of CH3(C≡C)5H. Enough rotational transitions from theK= 0 and 1 ladders were detected in either molecule to be confident of the identification and to determine the rotational and leading centrifugal distortion constants to high accuracy. Like other carbon chains, the two here may be important in combustion processes and may be detectable in the interstellar gas, where the two shortest methylpolyynes have already been observed.