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Video-and-language pre-training has shown promising results for learning generalizable representations. Most existing approaches usually model video and text in an implicit manner, without considering explicit structural representations of the multi-modal content. We denote such form of representations as structural knowledge, which express rich semantics of multiple granularities. There are related works that propose object-aware approaches to inject similar knowledge as inputs. However, the existing methods usually fail to effectively utilize such knowledge as regularizations to shape a superior cross-modal representation space. To this end, we propose a Cross-modaL knOwledge-enhanced Pre-training (CLOP) method with Knowledge Regularizations. There are two key designs of ours: 1) a simple yet effective Structural Knowledge Prediction (SKP) task to pull together the latent representations of similar videos; and 2) a novel Knowledge-guided sampling approach for Contrastive Learning (KCL) to push apart cross-modal hard negative samples. We evaluate our method on four text-video retrieval tasks and one multi-choice QA task. The experiments show clear improvements, outperforming prior works by a substantial margin. Besides, we provide ablations and insights of how our methods affect the latent representation space, demonstrating the value of incorporating knowledge regularizations into video-and-language pre-training.