A common assumption underlying the development of multi-echelon service models is that successive demands are independent. In this paper we study the robustness of two models, developed for a two-echelon serial inventory network, when the demand process is autocorrelated. Both stockpoints operate a periodic review order-up-to-S echelon inventory policy. Using an analytic approach, we extend the original models so that they apply exactly for any autocorrelated period demand process and explore the behaviour of the extended models under different scenarios. In order to study the effects of different autocorrelation characteristics, an MA(1) and an AR(1) process are analysed in detail. Our results demonstrate that, depending on the overall system parameters setting, models which ignore the effects of autocorrelation may provide very unsatisfactory estimates of the system performance. Hence, extreme caution is required when deciding the use of multi-echelon service models in practice.