Many real-world problems are encoded into SAT instances and efficiently solved by CDCL (Conflict-Driven Clause Learning) SAT solvers. However, some scenarios require distributed problem solving approaches. Privacy is often the main reason. This motivates the need to solve distributed SAT problems We analyze how this problem can be tacked in an efficient way, and present ABTSAT, a new version of the ABT (Asynchronous Backtracking) algorithm adapted to solve distributed SAT instances. It combines ABT execution with calls to CDCL SAT solvers and clause learning. ABTSAT is sound and complete, properties inherited from ABT, and solves local problems efficiently by using CDCL SAT solvers.