It has been shown that in crystals, near the Fermi resonance of optical exc
itons, in addition to the solitons discovered before, such as multi-exciton
bound complexes of cusp-, crater-, and dark-type possessing a single carri
er frequency, amplitude, and envelope, there are nonlinear soliton excitati
ons of a crucially new, breather-type. Such periodic soliton oscillations e
xhibit slowly pulsing amplitudes of high-frequency oscillations, with the c
arrier frequency being a multiple of the frequency of pulsations. In accord
ance with the multiplicity, the depth of pulsations defines a series of the
carrier frequencies, which are condensed near the basic frequency of optic
al oscillations. The spatial dependence of the two envelopes of new soliton
s of the cusp type is determined. With the increase in multiplicity, the sh
arpness of the space envelope of a soliton decreases, while the localizatio
n radius increases. Some other features of the solitons of new type are lis
ted. (C) 2000 MAIK "Nauka/ Interperiodica".