A strong node sequence for a directed graph G = (N, A) is a sequence of nodes containing every cycle-free path of G as a subsequence. A weak node sequence for G is a sequence of nodes containing every basic path in G as a subsequence, where a basic path nt, n~ ..... nj, is a path from Ilt to nk such that no proper subsequenee is a path from/nl to/.ik. (Every strong node sequence for G is a weak node sequence for G.) Kennedy has developed a global program data flow analysis method using node sequences. Kwiatowski and Kleitman have shown that any strong node sequence for the complete graph on n nodes must have length at least/.i 2 -0(n7~4 ยง for arbitrary positive e. Every graph on n nodes has a strong sequence of length/.i2. -2n + 4, so this bound is tight to within 0(n~4*'). However, the complete graph on n nodes has a weak node sequence of length 2n -1. In this paper, we show that for infinitely many n, there is a reducible flow graph G with n nodes (all with in-degree and out-degree bounded by two) such that any weak node sequence for G has length at least ~log~ n-O(n log log/.i). Aho and Ullman have shown that every reducible flow graph has a strong node sequence of length O(n log~ n); thus our bound is tight to within a constant factor for reducible graphs. We also show that for infinitely many n, there is a (non-reducible) flow graph H with n nodes (all with in-degree and out-degree bounded by two), such that any weak node sequence for H has length at least cn 2, where c is a positive constant. This bound, too, is tight to within a constant factor.