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We study large-amplitude oscillations of carbon nanotubes with chiralities$(m,0)$ and $(m,m)$ and predict the existence of localized nonlinear modes inthe form of {\em discrete breathers}. In nanotubes with the index $(m,0)$ {\emthree types} of localized modes can exist, namely longitudinal, radial, andtwisting breathers; however only the twisting breathers, or {\em twistons}, arenonradiating nonlinear modes which exist in the frequency gaps of the linearspectrum. Geometry of carbon nanotubes with the index $(m,m)$ allows only theexistence of broad radial breathers in a narrow spectral range.

Discrete Nonlinear Breathing Modes in Carbon Nanotubes