Cross-lingual entity alignment, which aims to precisely connect the same entities in different monolingual knowledge bases (KBs) together, often suffers challenges from feature inconsistency to sequence context unawareness. This paper presents a dual adversarial learning framework for cross-lingual entity alignment, DAEA, with two original contributions. First, in order to address the structural and attribute feature inconsistency between entities in two knowledge graphs (KGs), an adversarial kernel embedding technique is proposed to extract graph-invariant information in an unsupervised manner, and project two KGs into the common embedding space. Second, in order to further improve successful rate of entity alignment, we propose to produce multiple random walks through each entity to be aligned and mask these entities in random walks. With the guidance of known aligned entities in the context of multiple random walks, an adversarial knowledge translation model is developed to fill and translate masked entities in pairwise random walks from two KGs. Extensive experiments performed on real-world datasets show that DAEA can well solve the feature inconsistency and sequence context unawareness issues and significantly outperforms thirteen state-of-the-art entity alignment methods.