The thermal conductivity and the specific heat of several polymers and related materials are found to be not smooth functions in the temperature range between 30 and 50 K. A low‐temperature anomaly is observed. In the same temperature range, the mechanical and dielectric relaxation spectra of many polymers exhibit a cryogenic relaxation. It is suggested that both the cryogenic relaxation process and the anomaly of the thermal properties near 50 K are independent of the detailed chemical composition of the material and arise from the anisotropy of bonding forces in chain‐like or network‐like structures.