Electronic Journal of Differential Equations, Vol. 2010(2010), No. 36, pp. 1-12. Title: Neutral functional differential equations of second-order with infinite delays Authors: Runping Ye (Suqian College, Jiangsu, China) Guowei Zhang (Northeastern Univ., Shenyang, China) Abstract: This work shows the existence of mild solutions to neutral functional differential equations of second-order with infinite delay. The Hausdorff measure of noncompactness and fixed point theorem are used, without assuming compactness on the associated family of operators. Submitted November 24, 2009. Published March 09, 2010. Math Subject Classifications: 34K30, 34K40, 47D09. Key Words: Neutral functional differential equations; mild solution; Hausdorff measure of noncompactness; phase space.