Expressing the perturbation optical field in terms of module and phase, using the linearized nonlinear Schrodinger equation governing the evolution of perturbations, we have deduced the analytical expressions of the modules, phases, and gain coefficients of the perturbations with zero or cut-off frequency, and studied the evolutions of the two perturbations travelling along lossless optical fibers in the negative dispersion regime. The results indicate that the phase of the perturbation with zero (or cut-off) frequency increases (or decreases) with the propagation distance monotonously and tends to its asymptotic value nπ π/2 (or nπ) eventually. The evolution rates of the phases are closely related to the initial phase values. Although the asymptotic values of the field gain coefficients of the above mentioned two perturbations are equal to zero, and the increasing fashion of the modules is different from the familiar exponential type, it still suggests that the perturbations have a divergent nature when the propagation distance goes to infinity, indicating that the two kinds of perturbations can both lead to instability.