In the present paper we describe twu methods for solving singular perturbation problems. The idea behind these methods is the decomposition of the boundary layer function, i.e. the solution of such a problem can be expressed in the form u_ε(x)=w_ε(x)+v_ε(x)ρ(x), where ρ(x) is the boundary layer function, and w_ε(x) and v_ε(x) are in general smooth functions. Two methods are proposed for computing w_ε,v_ε.One is a mufti-iterative procedure, called the initial-value-problem method;the other is the boundary-value-problem method by wlhich one has to solve a pair of special buundary value problems. The error estimates and examples are included.