This paper explores the use of Constraint Logic Programming (CLP) as a platform for experimenting with planning problems in the presence of multiple interacting agents. The paper develops a novel constraint-based action language, B MAP, that enables the declarative description of large classes of multi-agent and multi-valued domains. B MAP supports several complex features, including combined effects of concurrent and interacting actions, concurrency control, and delayed effects. The paper presents a mapping of B MAP theories to CLP and it demonstrates the effectiveness of an implementation in SICStus Prolog on several benchmark problems. The effort is an evolution of previous research on using CLP for single-agent domains, demonstrating the flexibility of CLP technology to handle the more complex issues of multi-agency and concurrency.