Propagation of periodic cnoidal waves in a medium with a saturable nonlinea
r response is investigated, The ranges of existence of soliton solutions ar
e determined, and the specific features of such solutions are analysed with
in the limiting cases of strong and weak energy localisation in cnoidal wav
es. Optical multistability is discussed in the context of the existence of
periodic solutions, The stability of cnoidal waves is studied numerically a
nd analytically.