A class of non-symmetric indefinite problems from the point of view of multigrid algorithms is investigated. Some new uniform estimates for such an algorithm are developed. In particular the authors' interest is concentrated on a simple additive algorithm and on the multigrid \((V(1,0)\)-cycle) algorithms described by \textit{J. H. Bramble}, \textit{J. E. Pasciak} and \textit{I. Xu} [Math. Comput. 55, No. 191, 1-22 (1990; Zbl 0703.65076)]. The authors prove, without the assumption of full elliptic regularity, that these algorithms have a uniform reduction per iteration, independent of the finest mesh size and the number of refinement levels, provided that the coarsest mesh size is sufficiently small.