Water is absorbed by most polymers, but a change of properties is induced only in specific types of polymers. Water is considered to be present in the free volume and active only when attached to polymer chains by hydrogen bonds. The materials considered are PEI, PEEK, PES, PC, PA 12, and PA 6. The changes in damping spectra, moduli, and thermal expansion due to the moisture absorption have been investigated in the broad temperature range of 4.2-320 K. It is surprising that properties are changed by water in a different or opposite ways at low and high temperatures. Even at very low temperatures, absorbed water influences the mechanical performance in an unexpected way. The results at tow temperatures might be a tool for a better understanding of the features of the hydrogen bonded water, which itself could be a sensor for analysing molecular mobilities. The interpretation of results is generally not yet clear and some cryogenic results are in contradiction to well established correlations for dry polymers. Ideas for solving there problems are given in the conclusions of this study.