Title: Divergence-Regularized Multi-Agent Actor-Critic. Abstract: Entropy regularization is a popular method in reinforcement learning (RL). Although it has many advantages, it alters the RL objective and makes the converged policy deviate from the optimal policy of the original Markov Decision Process. Though divergence regularization has been proposed to settle this problem, it cannot be trivially applied to cooperative multi-agent reinforcement learning (MARL). In this paper, we investigate divergence regularization in cooperative MARL and propose a novel off-policy  cooperative MARL framework, divergence-regularized multi-agent actor-critic (DMAC). Mathematically, we derive the update rule of DMAC which is naturally off-policy, guarantees a monotonic policy improvement and is not biased by the regularization. DMAC is a flexible framework and can be combined with many existing MARL algorithms. We evaluate DMAC in a didactic stochastic game and StarCraft Multi-Agent Challenge and empirically show that DMAC substantially improves the performance of existing MARL algorithms. 