Soliton propagation along optical fibers is discussed on the basis of the modified nonlinear Schrödinger equation, which is known to be completely integrable in terms of the inverse-scattering transformation. Numerical observation of soliton propagation reveals various kinds of dynamical behavior, which cannot be accounted for by treating the nonlinear derivative term of the modified nonlinear Schrödinger equation as a perturbation term for the cubic nonlinear Schrödinger equation.