Existing emotional support conversation systems mainly focus on one-on-one seeker-supporter interactions and individual emotional states, leaving interpersonal relations in multi-party scenarios underexplored. In this work, we introduce relation-aware emotional support conversation, a new task that evaluates whether LLMs can capture and utilize the evolving dynamics of relationships to offer more effective emotional support. We construct RESCUE (Relation-aware Emotional Support Conversation Understanding and Evaluation Benchmark) from real couple and family interview conversations, containing