1The effect of environmental fluctuations is a major question in ecology. While it is widely 2 accepted that fluctuations and other types of disturbances can increase biodiversity, we have only a 3 limited understanding of the circumstances in which other types of outcomes can occur in a 4 fluctuating environment. Here we explore this question with laboratory microcosms, using 5 cocultures of two bacterial species, P. putida and P. veronii. At low dilution rates we observe 6 competitive exclusion of P. veronii, whereas at high dilution rates we observe competitive 7 exclusion of P. putida. When the dilution rate alternates between high and low, we do not observe 8 coexistence between the species, but rather alternative stable states, in which only one species 9survives and initial species' fractions determine the identity of the surviving species. The Lotka-10Volterra model with a fluctuating mortality rate predicts that this outcome is independent of the 11 timing of the fluctuations, and that the time-averaged mortality would also lead to alternative stable 12 states, a prediction that we confirm experimentally. Other pairs of species can coexist in a 13 fluctuating environment, and again consistent with the model we observe coexistence in the time-14 averaged dilution rate. We find a similar time-averaging result holds in a three-species 15 community, highlighting that simple linear models can in some cases provide powerful insight into 16 how communities will respond to environmental fluctuations. 17