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Inspired by the human brain's function and efficiency, neuromorphic computing offers a promising solution for a wide set of tasks, ranging from brain machine interfaces to real-time classification. The spiking neural network (SNN), which encodes and processes information with bionic spikes, is an emerging neuromorphic model with great potential to drastically promote the performance and efficiency of computing systems. However, an energy efficient hardware implementation and the difficulty of training the model significantly limit the application of the spiking neural network. In this work, we address these issues by building an SNNbased energy efficient system for real time classification with metal-oxide resistive switching random-access memory (R-RAM) devices. We implement different training algorithms of SNN, including Spiking Time Dependent Plasticity (STD-P) and Neural Sampling method. Our RRAM SNN systems for these two training algorithms show good power efficiency and recognition performance on realtime classification tasks, such as the MNIST digit recognition. Finally, we propose a possible direction to further improve the classification accuracy by boosting multiple SNNs.