The degree of the approximation represented by the basic equation of motion of a vibratory system influenced by internal damping was improved by the assumption that the damping coefficient is proportional to the n^th power of the strain (or stress) amplitude. The solution of the improved equation. was presented by use of approximate methods. The results were expressed in terms of the logarithmic decrement and specific damping to facilitate comparison with experimental data. Three theoretical curves were fitted to experimental curves of the logarithmic decrement. It was found that the theoretical curves accurately described the damping (that is, they fit the experimental curves) for low values of the strain. The curves were found to diverge for higher values of the strain. / M.S.