The authors consider second order autonomous difference equations of the form $z_{n+1}=f(z_n,z_{n-1})$. They establish strong sufficient conditions so that all solutions of this type of equations are attracted to period $2$-orbits. They also indicate how to built invariants or first integrals for these systems when all solutions converge to period-two solutions. (Reviewed for MathReviews, MathSciNet, 2006).