We investigate theoretically properties of partially coherent solitons in o
ptical nonlinear media with slow saturable nonlinearity. We have found nume
rically that such a medium can support spatial solitons which are asymmetri
c in shape and are composed of only a finite number of modes associated wit
h the self-induced waveguide. It is shown that these asymmetric spatial sol
itons can propagate many diffraction lengths without changes, but that coll
isions change their shape and may split them apart. [S1063-651X(99)12808-3]
.