# How to perform multigrid technique when relaxation methods don't converge?

It is well known that, when a system of linear equations is obtained from discretization of partial differential equation, the solution process can be accelerate significantly by multigrid technique. In the smoothing step of a multigrid cycle, relaxation method, such as Gauss-Seidel or Jacobi, is used. However, for relaxation method, convergence is only guaranteed for a limited class of matrices. For instance, the Gauss-Seidel Method only converges when the coefficient matrix is positive definite of diagonally dominant. My question is, if the coefficient matrix doesn't satisfy convergence requirement of relaxation method, is it still possible to perform multigrid technique? And, how to perform?