Electronic Journal of Differential Equations, Vol. 1999(1999), No. 31, pp. 1-12. Title: Asymptotic expansions for linear symmetric hyperbolic systems with small parameter Authors: O. Hawamdeh (Moldova State Univer., Moldova) A. Perjan (Moldova State Univer., Moldova) Abstract: The boundary layer functions method of Lyusternik-Vishik is used to obtain asymptotic expansions of the solutions to the Cauchy problem for linear symmetric hyperbolic systems with constant coefficients as the small parameter $\varepsilon$ tends to zero. Submitted March 22, 1999. Published September 9, 1999. Math Subject Classifications: 35B25, 35L45. Key Words: hyperbolic systems; asymptotic expansions; boundary layer functions; singular perturbations.