Neural language models (NLMs) such as recurrent neural networks or transformer models have led to great progress on many natural language processing benchmarks. However, when it comes to generating texts and responses in interactive settings, we still only have a very superficial understanding of whether these models can systematically produce coherent texts. In my talk, I'll present ongoing work on systematically evaluating English NLMs on one ability required for coherent discourse: determining whether an indefinite noun phrase introduces a new referent to the discourse. Inspired by Karttunen (1976), I'll present a behavioral experiment that can be performed with both humans and NLMs, which allows me to compare human and model behavior, and I'll discuss what results from these experiments can tell us about the discourse abilities of NLMs.