We study the degenerate semilinear elliptic systems of the form -div(h1(x)∇u) = λ(a(x)u + b(x)v) + Fu(x,u,v),x ∈ O,-div(h2(x)∇v) = λ(d(x)v + b(x)u) + Fv(x,u,v),x ∈ O,u |∂Ω = v|∂Ω = 0, where Ω ⊂ RN (N ≥ 2) is an open bounded domain with smooth boundary ∂Ω, the measurable, nonnegative diffusion coefficients h1, h2 are allowed to vanish in Ω (as well as at the boundary ∂Ω) and/or to blow up in O. Some multiplicity results of solutions are obtained for the degenerate elliptic systems which are near resonance at higher eigenvalues by the classical saddle point theorem and a local saddle point theorem in critical point theory. [ABSTRACT FROM AUTHOR]