It is known that, when two microbial populations competing for a single rate-limiting nutrient are grown in a spatially uniform environment, such as a single chemostat, with competition being the only interaction between them, they cannot coexist, but eventually one of the two populations prevails and the other becomes extinct. Spatial heterogeneity has been suggested as a means of obtaining coexistence of the two populations. A configuration of two interconnected chemostats is a simple model of a spatially heterogeneous environment. It has been shown that, when Monod's model is used for the specific growth rates of the two populations, steady-state coexistence can be obtained in such systems for wide ranges of operating conditions. In the present work, we study a model of microbial competition in configurations of interconnected chemostats and we show that, if a substrate inhibition model is used for the specific growth rates of the two populations, coexistence in a periodic state is also possible. The analysis of the model is done by numerical bifurcation theory methods.