Electronic Journal of Differential Equations, Vol. 2005(2005), No. 61, pp. 1-7. Title: Periodic solutions for planar systems with time-varying delays Authors: Chuangxia Huang (Hunan Univ., Changsha, China) Lihong Huang (Hunan Univ., Changsha, China) Yimin Meng (Hunan Univ., Changsha, China) Abstract: This paper concerns delay differential systems that can be regarded as a model of two-neuron artificial neural network with delayed feedback. Some interesting results are obtained for the existence of a periodic solution for the system. Our approach is based on the continuation theorem of coincidence degree, and a-priori estimates of the periodic solutions. Submitted September 22, 2004. Published June 10, 2005. Math Subject Classifications: 34K13, 92B20. Key Words: Differential system; neural network; periodic solution.