Let (M, \omega) be a Hamiltonian G-space with a momentum map F:M -> g^*. It is well-known that if \alpha is a regular value of F and G acts freely and properly on the level set F^{-1}(G\cdot\alpha), then the reduced space M_{\alpha}:=F^{-1}(G\cdot\alpha)/G is a symplectic manifold. We show that if the regularity assumptions are dropped the space M_{\alpha} is a union of symplectic manifolds, and that the symplectic manifolds fit together in a nice way. In other words the reduced space is a symplectic stratified space. This extends results known for the Hamiltonian action of compact groups.