We study self-action of light in parametric wave interactions in nonli
near quadratic media. We show the existence of stationary solitons in
the presence of Poynting vector beam walk-off or different group veloc
ities between the waves. We discover that the new solitons constitute
a two-parameter family, and they exist for different wave intensities
and transverse velocities. We discuss the properties of the walking so
litons and their experimental implications.