The compositionality of meaning extends beyond the single sentence. Just as words combine to form the meaning of sentences, so do sentences combine to form the meaning of paragraphs, dialogues and general discourse. We introduce both a sentence model and a discourse model corresponding to the two levels of compositionality. The sentence model adopts convolution as the central operation for composing semantic vectors and is based on a novel hierarchical convolutional neural network. The discourse model extends the sentence model and is based on a recurrent neural network that is conditioned in a novel way both on the current sentence and on the current speaker. The discourse model is able to capture both the sequentiality of sentences and the interaction between different speakers. Without feature engineering or pretraining and with simple greedy decoding, the discourse model coupled to the sentence model obtains state of the art performance on a dialogue act classification experiment.