Carbon composites (carbon-aramide) constitute modern “Hi-Tech” materials of an extremely favourable ratio of load to mass transfer. Thereby the idea of using them for long transmission shafts seems to be very attractive, specially in aviation and sailing. Unfortunately structures made of carbon-aramide composites are characterised by a strong anisotropy and in effect by non-linearity of elastic characteristics, due to which they have significantly different dynamic influences than steel structures. To this end there is a need of application of different calculation algorithms than the ones widely used in Construction Engineering. It requires taking into account the coupling between transverse and torsional vibrations, which essentially projects onto the possibility of the critical states occurrence. This is indispensable since shafts made of expensive composite materials are profitable in places where their low elementary mass is essential (long high-speed transmission systems). The paper presents the theoretical discussion of this problem, empirical investigations of nonlinear characteristics as well as the proposition of designing methods.