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This paper proposes a new model of an Evolving Spiking Neural Network (ESNN) for spatio-temporal data (STD) classification problems. The proposed ESNN model incorporates an additional layer for capturing both spatial and temporal components of the STD and then transforms them into high dimensional spiking patterns. These patterns are learned and classified in the evolving classification layer of the ESNN. A fast time-to-first-spike learning algorithm is used that enables the new model to be more suitable for learning from the STD streams in an adaptive and incremental manner. The proposed method is evaluated on a benchmark sign language video that is spatio-temporal in nature. The results show that the proposed method is able to capture important spatio-temporal information from the STD stream. This results in significantly higher classification accuracy than the traditional time-delay MLP neural network model. Future directions for the development of ESNN models for STD are discussed.