In the talk the Multigrid appraoch is analysed for ill-conditioned Block Toeplitz matrices. Thereby prolongations and restrictions are constructed depending on the zeroes of the generating function of the matrix. This function is a matrix function in the block case and a function of two or more variables in the multilevel case. Especially we consider indefinite problems or underlying functions with an infinite number of zeroes. Because Toeplitz matrices can also be seen as Block Toeplitz matrices, this approach also leads to new Multigrid methods for Toeplitz matrices. On numerical examples we compare different choices for prolongations and restrictions.