In this paper we study the existence theorem for solution of the nonlinear degenerate oblique boundary value problems for second order fully nonlinear elliptic equations F(x, u, Du, D²u) = 0 \quad x ∈ Ω, G(x, u, D, u) = 0, \qquad x ∈ ∂Ω where F (x, z, p, r) satisfies the natural structure conditions, G (x, z, q) satisfies G_q ≥ 0, G_x ≤ - G_0 < 0 and some structure conditions, vector τ is nowhere tangential to ∂Ω. This result extends the works of Lieberman G. M., Trudinger N. S. [2], Zhu Rujln [1] and Wang Feng [6].
