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Human generates responses relying on semantic and functional dependencies, including coreference relation, among dialogue elements and their context. In this paper, we investigate matching a response with its multi-turn context using dependency information based entirely on attention. Our solution is inspired by the recently proposed Transformer in machine translation (Vaswani et al., 2017) and we extend the attention mechanism in two ways. First, we construct representations of text segments at different granularities solely with stacked self-attention. Second, we try to extract the truly matched segment pairs with attention across the context and response. We jointly introduce those two kinds of attention in one uniform neural network. Experiments on two large-scale multi-turn response selection tasks show that our proposed model significantly outperforms the state-of-the-art models.