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Generalization to previously unseen images with potential domain shifts and different styles is essential for clinically applicable medical image segmentation, and the ability to disentangle domain-specific and domain-invariant features is key for achieving Domain Generalization (DG). However, existing DG methods can hardly achieve effective disentanglement to get high generalizability. To deal with this problem, we propose an efficient Contrastive Domain Disentanglement and Style Augmentation (CDDSA) framework for generalizable medical image segmentation. First, a disentangle network is proposed to decompose an image into a domain-invariant anatomical representation and a domain-specific style code, where the former is sent to a segmentation model that is not affected by the domain shift, and the disentangle network is regularized by a decoder that combines the anatomical and style codes to reconstruct the input image. Second, to achieve better disentanglement, a contrastive loss is proposed to encourage the style codes from the same domain and different domains to be compact and divergent, respectively. Thirdly, to further improve generalizability, we propose a style augmentation method based on the disentanglement representation to synthesize images in various unseen styles with shared anatomical structures. Our method was validated on a public multi-site fundus image dataset for optic cup and disc segmentation and an in-house multi-site Nasopharyngeal Carcinoma Magnetic Resonance Image (NPC-MRI) dataset for nasopharynx Gross Tumor Volume (GTVnx) segmentation. Experimental results showed that the proposed CDDSA achieved remarkable generalizability across different domains, and it outperformed several state-of-the-art methods in domain-generalizable segmentation.