Long-term memory is essential for conversational agents to maintain coherence, track persistent tasks, and provide personalized interactions across extended dialogues. However, existing approaches as Retrieval-Augmented Generation (RAG) and graph-based memory mostly rely on pairwise relations, which can hardly capture high-order associations, i.e., joint dependencies among multiple elements, causing fragmented retrieval. To this end, we propose HyperMem, a hypergraph-based hierarchical memory architecture that explicitly models such associations using hyperedges. Particularly, HyperMem structures memory into three levels: topics, episodes, and facts, and groups related episodes and their facts via hyperedges, unifying scattered content into coherent units. Leveraging this structure, we design a hybrid lexical-semantic index and a coarse-to-fine retrieval strategy, supporting accurate and efficient retrieval of high-order associations. Experiments on the LoCoMo benchmark show that HyperMem achieves state-of-the-art performance with 92.73% LLM-as-a-judge accuracy, demonstrating the effectiveness of HyperMem for long-term conversations.