  We analyze the influence of spectrally modulated dispersion and loss on the
stability of mode-locked oscillators. In the negative dispersion regime, a
soliton oscillator can be stabilized in a close proximity to zero-dispersion
wavelength, when spectral modulation of dispersion and loss are strong and
weak, respectively. If the dispersion is close to zero but positive, we observe
chaotic mode-locking or a stable coexistence of the pulse with the CW signal.
The results are confirmed by experiments with a Cr:YAG oscillator.
