The aim of this paper is to study the dynamical behavior of positive solutions for a system of rational difference equations of the following form: u(n+1) = alpha u(n-1)/(beta + gamma v(n-2)(p)), v+1 = alpha(1)v(n-1)/(beta(1) + gamma(1)u(n-2)(p)), n = 0, 1, . . ., where the parameters alpha, beta, gamma, alpha(1), beta(1), gamma(1), p and the initial values u(-i), v(-i) for i = 0, 1, 2 are positive real numbers.