Emotion recognition in conversations is crucial for the development of empathetic machines. Present methods mostly ignore the role of inter-speaker dependency relations while classifying emotions in conversations. In this paper, we address recognizing utterance-level emotions in dyadic conversational videos. We propose a deep neural framework, termed conversational memory network, which leverages contextual information from the conversation history. The framework takes a multimodal approach comprising audio, visual and textual features with gated recurrent units to model past utterances of each speaker into memories. Such memories are then merged using attention-based hops to capture inter-speaker dependencies. Experiments show an accuracy improvement of 3–4% over the state of the art.