Described herein are anisotropic polymer composites, made up of (cyanoethylpropyl)cellulose (CEPC) and acrylic polymer. A band texture (which can be seen with a polarisation microscope) forms in CEPC and its lyotropic solutions in acrylic monomer after orientation as a result of relaxation phenomena. The photopolymerisation of acrylic monomer (acrylic or methacrylic acid) in an oriented lyotropic solution of CEPC 'freezes' the orientation, and stable birefringent polymer composites are created. Thermooptical analysis shows that these composites exhibit thermally reversible anisotropy of optical properties. Molecular relaxations in such composites were investigated by means of dielectric and mechanical spectroscopies. The molecular relaxation processes, characteristic of pure components, are preserved in these composites. Two representations were used in dielectric spectroscopy: the temperature dependences of dielectric loss epsilon" and of electric modulus M". The latter was especially useful in the high temperature range, where ionic conductivity dominates the dielectric response.