Dispersions were studied of multiwall carbon nanotubes in cholesteric liquid crystals of three types: nematics with chiral dopant, mixtures of cholesterol derivatives, and similar mixtures close to smectic-A transition. In the first two cases, no appreciable effects of nanotubes upon selective reflection spectra were noted, while optical transmission increased significantly at the isotropic phase transition. Aromatic and steroid matrices differed significantly in this respect, though in both cases the nanotubes were apparently oriented along the directors of quasi-nematic layers. In the third case, nanotubes slightly but clearly affected the measured selective reflection peaks, suggesting suppression of the smectic-A phase formation.