The huge theoretical and empirical econometric literatures on long memory and on structural change have evolved largely independently, as the phenomena appear distinct. We argue, in contrast, that they are intimately related. In particular, we show analytically that stochastic regime switching is easily confused with long memory, so long as only a “small” amount of regime switching occurs (in a sense that we make precise). A Monte Carlo analysis supports the relevance of the asymptotic theory in finite samples and produces additional insights.