AbstractStalling in the simplex algorithm is defined as an exponentially long sequence of consecutive degenerate pivots without cycling. Pivot rules for the network simplex algorithm that prevent both cycling and stalling are considered. For several of these, the number of consecutive degenerate pivots is shown to be at mostk(k+ 1)/2, wherekis the number of degenerate basic variables. The relationship between these pivot rules for the network simplex algorithm and strongly polynomial simplex variants for solving the shortest path problem is also discussed.