Two relaxation-algorithms and a number of restriction/prolongation-processes are compared within a non-linear FAS multi-grid research code. Paper focuses on the choice of relaxationalgorithm, which should be fast, robust (stable convergence for all local flow directions) and insensitive (good short wave damping for all possible mesh ratios). A mixed Incomplete Lower Upper decomposition/Strongly Implicit Procedure (ILU/SIP) algorithm appears to fulfill these requirements to a much higher degree than present SLOR algorithms. This new algorithm involves only one free parameter, which can be set once and for all. Numerical results will be presented for a transonic small disturbance equation solved for the flow in "a windtunnel with a bump on the bottom".