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In unsupervised domain adaptation, rich domain-specific characteristics bring great challenge to learn domain-invariant representations. However, domain discrepancy is considered to be directly minimized in existing solutions, which is difficult to achieve in practice. Some methods alleviate the difficulty by explicitly modeling domain-invariant and domain-specific parts in the representations, but the adverse influence of the explicit construction lies in the residual domain-specific characteristics in the constructed domain-invariant representations. In this paper, we equip adversarial domain adaptation with Gradually Vanishing Bridge (GVB) mechanism on both generator and discriminator. On the generator, GVB could not only reduce the overall transfer difficulty, but also reduce the influence of the residual domain-specific characteristics in domain-invariant representations. On the discriminator, GVB contributes to enhance the discriminating ability, and balance the adversarial training process. Experiments on three challenging datasets show that our GVB methods outperform strong competitors, and cooperate well with other adversarial methods. The code is available at https://github.com/cuishuhao/GVB.