Entity and relation extraction is a conventional task in the field of information extraction. Existing work primarily focuses on detecting specific relations between entities, often constrained to particular fields and lacking general applicability. In response, we propose a novel task: nominal compound relation extraction (NCRE), which concentrates on abstract and broadly applicable relation extraction between noun phrases. This task diverges significantly from traditional entity and relation extraction in two key respects. Firstly, our task involves general nominal compounds rather than named entities, which are longer and encompass a broader scope, presenting significant challenges for extraction. Secondly, relation extraction in NCRE demands an in-depth understanding of context to detect abstract relations. We manually annotate a high-quality Chinese dataset for the NCRE task and develop a model incorporating the rotary position-enhanced word pair (RoWP) detection schema. Experimental results demonstrate the efficiency of our RoWP model over previous baselines, while the suboptimal F1 scores indicate that NCRE remains a challenging task. Our code and data are available at https://github.com/yeecjc/NCRE.