Conversational sentiment analysis (CSA) and emotion-cause pair extraction (ECPE) tasks have attracted increasing attention in recent years. The former aims to predict the sentiment states of speakers in a conversation, and the latter is about extracting emotion-cause clauses in a document. However, one drawback of CSA is that it cannot model the causal reasoning among emotion and neutral utterances from different speakers. In this work, we propose a new task: emotion-cause pair extraction in conversations (ECPEC), which aims to extract pairs of emotional utterances and corresponding cause utterances in conversations. The utterance-level ECPEC task is more challenging since the distance between emotion and cause utterances is larger than that of the clause-level ECPE task. To this end, we build a novel dataset ConvECPE and propose a specifically designed two-step framework for the new ECPEC task. Experimental results on ConvECPE dataset demonstrate the feasibility of the ECPEC task as well as the effectiveness of our framework.