We deploy the methods of controlled psycholinguistic experimentation to shed light on the extent to which the behavior of neural network language models reflects incremental representations of syntactic state. To do so, we examine model behavior on artificial sentences containing a variety of syntactically complex structures. We test four models: two publicly available LSTM sequence models of English (Jozefowicz et al., 2016; Gulordava et al., 2018) trained on large datasets; an RNNG (Dyer et al., 2016) trained on a small, parsed dataset; and an LSTM trained on the same small corpus as the RNNG. We find evidence that the LSTMs trained on large datasets represent syntactic state over large spans of text in a way that is comparable to the RNNG, while the LSTM trained on the small dataset does not or does so only weakly.