he discretization of the Stokes equations with the mini-element yields a linear system of equations whose system matrix is symmetric and indefinite. It has two symmetric blocks, one of which is positive definite, the other negative definite. A change of sign in the second block destroys the symmetry but the resulting matrix is coercive. We discuss different conjugate gradient-like algorithms for these two systems, and compare the storage and work requirements. The numerical results of several test examples are given.