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 ‖λ(H)1r−λ(W)1r‖/λ(H)1r ∝λ0 is satisfied near the neutral state, where λ(H)1r and λ(W)1r are the real parts of the first Landau constant defined by the methods of Herbert and Watson, respectively, and λ0 is the linear growth rate. This conclusion is consistent with the error estimation by Herbert, but is more accurate.