2005-Oujda International Conference on Nonlinear Analysis, Oujda, Morocco. Electronic Journal of Differential Equations, Conference 14 (2006), pp. 21-33. Title: Limit behavior of an oscillating thin layer Authors: Abdelaziz Ait Moussa (Univ. Mohammed 1er, Oujda, Morocco) Jamal Messaho (Univ. Mohammed 1er, Oujda, Morocco) Abstract: We study the limit behavior of a thermal problem, of a containing structure, an oscillating thin layer of thickness and conductivity depending of $\varepsilon$. We use the the epi-convergence method to find the limit problems with interface conditions. The obtained results are tested numerically. Published September 20, 2006. Math Subject Classifications: 35B40, 82B24, 76M50. Key Words: Limit behavior; epi-convergence method; limit problems.