Summary: This paper develops a framework for averaging functional-differential equations (FDEs) with fast and slow time scales. First, partial averaging is presented for two-time scale systems, where averaging performed on the fast time system, while slow time is ‘frozen.’ This creates an averaged equation which is slowly time-varying, hence the terminology of partial averaging. We show that solutions of the original FDE and its corresponding partially averaged equation remain close on arbitrarily long but finite time intervals. Assuming that the partially averaged system has an exponentially stable equilibrium point, the closeness results are extended to infinite time intervals. Next, we study the case when there are both fast and slow states. When the fast states decay quickly to equilibrium points, the system can be viewed as a perturbation of an FDE with fast and slow time scales. Then, partial averaging results can be applied. Classes of periodic systems are studied in which conditions of the averaged equation guarantee the existence of unique periodic solutions. Results are given for discrete-time delay difference equations, too.