When a molecule is dissociated through separate excitations by one or two polarized photons the fragment distribution is forward-backward symmetric with respect to the polarization axis. However,if the molecule is simultaneously excited by optical electric fields, E(omega) and E(2 omega), the amplitude for excitation is a sum of an amplitude for absorbing one photon of frequency 2 omega and an amplitude for absorbing two; photons of frequency omega, When the sum is squared to obtain the fragment angular distribution, there is a cross product which depends on the phase difference Delta phi = phi(2 omega) - 2 phi(omega). With suitable adjustment of the relative intensities at the two frequencies large unidirectionality can be obtained. The left-right anisotropy on the polarization axis depends on the symmetry of the transitions, real and virtual. In the most favorable case 97% of a particular fragment is ejected in one hemisphere and only 3% in the other. In a less favorable case 60% of the fragment is ejected in one hemisphere. (C) 1997 American Institute of Physics.