In this paper, the homotopy perturbation and Adomain0 s decom-
position methods are applied to obtain the approximate solutions of the equa-
tion of motion and heat equation for the harmonic waves propagation in a non-
linear generalized thermoelasticity with magnetic Öeld. The problem is solved in one-dimensional elastic half-space model sub jected initially to a prescribed harmonic displacement and the temperature of the medium. The displace-
ment and temperature are calculated for the two methods with the variations of the magnetic Öeld and the relaxation times considering Green Lindsay the-
ory (GL). The results obtained are displayed graphically to show the ináuences of the new parameters and the differences between the methods technique. It is
obvious that the homotopy perturbation method and adomain decomposition
method gives the same results that indicate the origin of the approximate
solutions and the methods powerful.