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Analog implementation of Oscillatory Neural Networks (ONNs) has the potential to implement fast and ultra-low-power computing capabilities. One of the drawbacks of analog implementation is component mismatches which cause desynchronization and instability in ONNs. Emerging devices like memristors and VO2 are particularly prone to variations. In this paper, we study the effect of component mismatches on the performance of differential ONNs (DONNs). Mismatches were considered in two main blocks: differential oscillatory neurons and synaptic circuits. To measure DONN tolerance to mismatches in each block, performance was evaluated with mismatches being present separately in each block. Memristor-bridge circuits with four memristors were used as the synaptic circuits. The differential oscillatory neurons were based on VO2-devices. The simulation results showed that DONN performance was more vulnerable to mismatches in the components of the differential oscillatory neurons than to mismatches in the synaptic circuits. DONNs were found to tolerate up to 20% mismatches in the memristance of the synaptic circuits. However, mismatches in the differential oscillatory neurons resulted in non-uniformity of the natural frequencies, causing desynchronization and instability. Simulations showed that 0.5% relative standard deviation (RSD) in natural frequencies can reduce DONN performance dramatically. In addition, sensitivity analyses showed that the high threshold voltage of VO2-devices is the most sensitive parameter for frequency non-uniformity and desynchronization.