Electronic Journal of Differential Equations, Vol. 2000(2000), No. 25, pp. 1-14. Title: A classification scheme for positive solutions of second order nonlinear iterative differential equations Authors: Xianling Fan (Lanzhou Univ., Lanzhou, P. R. China) Wan-Tong Li (Lanzhou Univ., Lanzhou, P. R. China) Chengkui Zhong (Lanzhou Univ., Lanzhou, P. R. China) Abstract: This article presents a classification scheme for eventually-positive solutions of second-order nonlinear iterative differential equations, in terms of their asymptotic magnitudes. Necessary and sufficient conditions for the existence of solutions are also provided. Submitted December 11, 1999. Published March 31, 2000. Math Subject Classifications: 34K15. Key Words: Nonlinear iterative differential equation; oscillation; eventually positive; asymptotic behavior.