We propose to generalize language models for conversational speech recognition to allow them to operate across utterance boundaries and speaker changes, thereby capturing conversation-level phenomena such as adjacency pairs, lexical entrainment, and topical coherence. The model consists of a long-short-term memory (LSTM) recurrent network that reads the entire word-level history of a conversation, as well as information about turn taking and speaker overlap, in order to predict each next word. The model is applied in a rescoring framework, where the word history prior to the current utterance is approximated with preliminary recognition results. In experiments in the conversational telephone speech domain (Switchboard) we find that such a model gives substantial perplexity reductions over a standard LSTM-LM with utterance scope, as well as improvements in word error rate.