Let \(\Delta\) and \(\Delta\) ’ be CCR-algebras over nondegenerate symplectic spaces. The central limit theorem tells about the limit of \(T^ n\circ \Phi_ n\) (with an appropriate cutting off) where \(T: \Delta\) \(\to \Delta '\) is a completely positive even unit preserving mapping and \(\Phi_ n:\Delta \to \Delta^ n=\otimes^{n}_{1}\Delta\) is a specified homomorphism. Quasi-free completely positive mappings turn out to be the noncommutative analogue of gaussian distributions since they appear in the central limit. If T is a state then \(T^ n\circ \Phi_ n\) converges pointwise to an even quasi-free state. The construction of the central limit goes as in the case of the CAR-algebra but in the CCR different technical problems arise.