A mathematical derivation is given of the dielectric properties of systems containing straight polar chains such that to each value of the total moment of a chain there corresponds only one arrangement of its dipoles. If the moments of the individual dipoles and the probability of an elementary transition are fixed, both the total dielectric loss and the effective relaxation time of the system increase in proportion to the square of the number of states of each chain. These conclusions are not valid for kinked chains and apply only qualitatively if the chains are branched. The theory provides an explanation for the high dielectric losses at low frequencies observed in many solids containing hydroxyl groups. It can further explain the low frequency absorption found in ionic crystals containing lattice imperfections ; in this interpretation the theory is related to Jaffe's theory of conductivity in polarizable media.