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Unsupervised Domain adaptation (UDA) attempts to recognize the unlabeled target samples by building a learning model from a differently-distributed labeled source domain. Conventional UDA concentrates on extracting domain-invariant features through deep adversarial networks. However, most of them seek to match the different domain feature distributions, without considering the task-specific decision boundaries across various classes. In this paper, we propose a novel Adversarial Dual Distinct Classifiers Network (AD$^2$CN) to align the source and target domain data distribution simultaneously with matching task-specific category boundaries. To be specific, a domain-invariant feature generator is exploited to embed the source and target data into a latent common space with the guidance of discriminative cross-domain alignment. Moreover, we naturally design two different structure classifiers to identify the unlabeled target samples over the supervision of the labeled source domain data. Such dual distinct classifiers with various architectures can capture diverse knowledge of the target data structure from different perspectives. Extensive experimental results on several cross-domain visual benchmarks prove the model's effectiveness by comparing it with other state-of-the-art UDA.