We introduce a novel class of parametric optical solitons supported simulta
neously by two second-order nonlinear cascading processes, second-harmonic
generation and sum-frequency mixing. We obtain analytical and numerical sol
utions for three-wave spatial solitons and show that the presence of an add
itional cascading mechanism can change dramatically the properties and stab
ility of two-wave quadratic solitary waves. (C) 1999 Optical Society of Ame
rica.