In massively parallel computational tasks, such as pattern recognition, conventional computing architectures have insufficient power efficiency for energy constrained environments. This has made alternative architectures, such as neuromorphic computing, increasingly attractive. Oscillatory neural networks (ONNs) are one promising architecture, but efficient hardware implementations have been limited by shortcomings in CMOS technology, specifically in the efficient implementation of oscillators and synaptic weights. The authors have recently demonstrated that metal-oxide based resistive switching (RRAM) structures can be engineered to create low-power, scalable, voltage-controlled oscillators that utilize inherent meta-stability in the device. This work proposes an RRAM-based ONN that couples oscillatory "neurons" through weighted "synapses" using oscillator phase as the state-variable. This paper demonstrates a robust architecture using only a few logic gates per neuron to implement phase initialization and locking of these oscillators, and demonstrate their capability to identify stored patterns from noisy inputs. Using measured characteristics of RRAMs as oscillators and programmable resistors, compact models are derived and used to simulate both an 8-neuron and 20-neuron network.Index Terms-Metal-oxide resistive memory, neuromorphic computing, oscillatory neural networks, RRAM-based nano-oscillators.