Electronic Journal of Differential Equations, Vol. 2010(2010), No. 151, pp. 1-8. Title: Existence of solutions to n-th order neutral dynamic equations on time scales Authors: Qiaoluan Li (Hebei Normal Univ., Shijiazhuang, China) Zhenguo Zhang (Hebei Normal Univ., Shijiazhuang, China) Abstract: In this article, we study n-th order neutral nonlinear dynamic equation on time scales. We obtain sufficient conditions for the existence of non-oscillatory solutions by using fixed point theory. Submitted June 6, 2010. Published October 21, 2010. Math Subject Classifications: 34K40, 34N99, 39A10. Key Words: Time scales; dynamic equations; non-oscillatory solution.