We present persona-based models for handling the issue of speaker consistency in neural response generation. A speaker model encodes personas in distributed embeddings that capture individual characteristics such as background information and speaking style. A dyadic speakeraddressee model captures properties of interactions between two interlocutors. Our models yield qualitative performance improvements in both perplexity and BLEU scores over baseline sequence-to-sequence models, with similar gains in speaker consistency as measured by human judges.