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Automatic identification of foreign accents is valuable for many speech systems, such as speech recognition, speaker identification, voice conversion, etc. The INTERSPEECH 2016 Native Language Sub-Challenge is to identify the native languages of non-native English speakers from eleven countries. Since differences in accent are due to both prosodic and articulation characteristics, a combination of long-term and short-term training is proposed in this paper. Each speech sample is processed into multiple speech segments with equal length. For each segment, deep neural networks (DNNs) are used to train on long-term statistical features, while recurrent neural networks (RNNs) are used to train on short-term acoustic features. The result for each speech sample is calculated by linearly fusing the results from the two sets of networks on all segments. The performance of the proposed system greatly surpasses the provided baseline system. Moreover, by fusing the results with the baseline system, the performance can be further improved.