In this paper,the higher order asymptotic behaviors of boundary blow-up solutions to the equation Δu = up ±丨▽u丨q in bounded smooth domain Ω ? RN are systematically investigated for p and q.The second and third order boundary behaviours of the equation are derived.The results show the role of the mean curvature of the boundary ?Ω and its gradient in the high order asymptotic expansions of the solutions.