We investigate analytically and numerically the existence and stability pro
perties of three-wave solitons resulting from double-resonance (type I plus
type II) parametric interaction in a purely quadratic nonlinear medium. Th
e existence of a family of stable solitons for the double-resonance model i
s demonstrated in a broad parameter range. Moreover, these solitons are sho
wn to exhibit multistability, a feature that is potentially useful for opti
cal switching applications. Finally, we find and present a novel family of
quasi solitons. (C) 1999 Optical Society of America.