Two kinds of nonlinear stability theories are examined, Herbert’s method [J. Fluid Mech.126, 167 (1983)] and that of Watson [J. Fluid Mech.9, 371 (1960)]. They are compared by calculating the first Landau constant of plane Poiseuille flow numerically according to their definitions. It is found that ‖&lgr;(H)1r−&lgr;(W)1r‖/&lgr;(H)1r∝&lgr;0is satisfied near the neutral state, where &lgr;(H)1rand &lgr;(W)1rare the real parts of the first Landau constant defined by the methods of Herbert and Watson, respectively, and &lgr;0is the linear growth rate. This conclusion is consistent with the error estimation by Herbert, but is more accurate.