Echo state networks (ESNs) are recurrent neural networks that can be trained efficiently because the weights of recurrent connections remain fixed at random values. Investigations of these networks' ability to generalize in sentence-processing tasks have resulted in mixed outcomes. Here, we argue that ESNs do generalize but that they are not systematic, which we define as the ability to generally outperform Markov models on test sentences that violate the training sentences' grammar. Moreover, we show that systematicity in ESNs can easily be obtained by switching from arbitrary to informative representations of words, suggesting that the information provided by such representations facilitates connectionist systematicity.