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We demonstrate the first hardware implementation of an oscillatory neural network (ONN) utilizing resistive memory (ReRAM) for coupling elements. A ReRAM crossbar array chip, integrated into the Back End of Line (BEOL) of CMOS technology, is leveraged to establish dense coupling elements between oscillator neurons, allowing phase-encoded analog information to be processed in-memory. We also realize an ONN architecture design with the coupling ReRAM array. To validate the architecture experimentally, we present a conductive metal oxide (CMO)/HfOx ReRAM array chip integrated with a 2-by-2 ring oscillator-based network. The system successfully retrieves patterns through correct binary phase locking. This proof of concept underscores the potential of ReRAM technology for large-scale, integrated ONNs.