This paper investigates the exponential synchronization of linearly coupled ordinary differential systems.The intrinsic nonlinear dynamics may not satisfy the QUAD condition or weak-QUAD condition.First,it gives a new method to analyze the exponential synchronization of the systems.Second,two theorems and their corollaries are proposed for the local or global exponential synchronization of the coupled systems.Finally,an application to the linearly coupled Hopfield neural networks and several simulations are provided for verifying the effectiveness of the theoretical results.