Abstract Constrained multiobjective optimization problems (CMOPs) are challenging for evolutionary algorithms (EAs). Due to the interaction of multiple constraints, the constrained Pareto fronts (CPFs) exhibit various complex characteristics, e.g., degeneracy, discontinuous or low feasible ratio. Most algorithms achieve poor convergence and diversity performance on these problems. Therefore, we proposed a coevolutionary framework based on constraints decomposition to solve the complex CMOPs. Specifically, this framework decomposes the CMOP into multiple help subproblems with single constraint, thereby decoupling the complex constraints. Then, the subpopulations optimize these subproblems to assist in solving the original problem. Furthermore, to avoid wasting computational resources, a two-stage strategy was used to fully utilize the auxiliary populations to search for feasible solutions. And an evolutionary state detection strategy based on historical information is proposed, which is used to determine whether the evolution moves to the next stage. The framework can take the advantage of the low complexity of single-constraint problems to help algorithm search the complete feasible regions. Experiments on benchmark problems show that the proposed algorithm is competitive with five other most representative constrained evolutionary algorithms in terms of convergence and diversity performance.