Electronic Journal of Differential Equations, Vol. 2004(2004), No. 93, pp. 1-15. Title: Existence of solutions for a nonlinear degenerate elliptic system Authors: Nguyen Minh Chuong (Academy of Science and Technology, Vietnam) Tran Dinh Ke (Hanoi Univ. of Education, Vietnam) Abstract: In this paper, we study the existence of solutions for degenerate elliptic systems. We use the sub-super solution method, and the existence of classical and weak solutions. Some sub-supersolutions are constructed explicitly, when the nonlinearities have critical or supercritical growth. Submitted February 18, 2004. Published July 27, 2004. Math Subject Classifications: 34B27, 35J60, 35B05. Key Words: Subsolution; supersolution; degenerate elliptic equation.