Numerical and experimental studies of the consequences of fluctuations in pulse peak power to the single-pass pulse evolution of subpicosecond pulses near the zero-dispersion wavelength are described, where the pulse fluctuations originate from the source. A numerical model is presented for determining the average spectral behavior of fluctuating pulses when the statistical distribution of injected peak powers is known. A few calculated examples are presented for the case of a Gaussian distribution of peak powers.