Emotion-Cause Pair Extraction (ECPE) task aims to pair all emotions and corresponding causes in documents.ECPE is an important task for developing human-like responses. However, previous ECPE research is conducted based on news articles, which has different characteristics compared to dialogues. To address this issue, we propose a Pair-Relationship Guided Mixture-of-Experts (PRG-MoE) model, which considers dialogue features (e.g., speaker information).PRG-MoE automatically learns relationship between utterances and advises a gating network to incorporate dialogue features in the evaluation, yielding substantial performance improvement. We employ a new ECPE dataset, which is an English dialogue dataset, with more emotion-cause pairs in documents than news articles. We also propose Cause Type Classification that classifies emotion-cause pairs according to the types of the cause of a detected emotion. For reproducing the results, we make available all our code and data.