Аннотация:The dispersion curves for harmonic waves in composite cylindrical elastic solids with a coating, made of non traditional soft material (nematic elastomer) are investigated. The obtained earlier low frequency effective model of nematics is used with taking into account the anisotropy, viscosity and internal rotation of long molecules of material. The impedance matrices, dispersion equations and asymptotics of speeds and wavenumbers in the long-wave approximation are derived for the further numerical analysis. The obtained quasi resonance effects of the first and of the second kinds are discussed for waves of different polarization.