Abstract: In this paper.the following mixed boundary value problem for second-order system of differential equations of the elliptic type will be discussed to find the function u and v such that they satisfy:
[(¹₀⁰_λ)(∂²)/(∂x²)+(_λ-1⁰₀^λ-1)(∂²)/(∂x∂y)+(^λ₀¹₀(∂²)/(∂y²)](_v^u)
+(_d21(x,y)^d₁₁(x,y)_d22(x,y)^d₁₂(x,y))[¹₀⁰₁(∂/∂x)+(⁰₁^-1₀)(∂/∂y)](_v^u)=(_f2^f₁)(1)
u|c=g(z),(2)
Σ^-1f_c((∂u)/(∂y)+(∂v)/(∂x))δ(s)ds=k₁,(7')
v(z_η)=k₂,(13)
The solution of this problem is found by means of the theory of generalized analytic function and the integral equation method for solving boundary value problems.

Key words: elliptic type, differential eguation, boundary value problem