Constrained multiobjective optimization problems (CMOPs) are prevalent in various real-world applications, presenting a formidable challenge to existing evolutionary algorithms when faced with intricate constraints. When solving CMOPs, a crucial concern is achieving a balance between convergence, diversity, and feasibility. To address these challenges, this paper proposes a two-archive-based constrained multiobjective competitive swarm optimizer. The algorithm preserves two collaborative and complementary archives to improve population convergence and feasibility. By implementing a competitive particle swarm mechanism, offspring solutions are generated by drawing upon solutions from both archives, thus capitalizing on their synergistic effect and exceptional information. An adaptive parameter is also used to adjust the bias in choosing the winner in the paired competition during the evolution. The experimental results demonstrate the effectiveness of the proposed algorithm in handling constrained multiobjective optimization problems.