  We show that dynamic exchange is a dominant effect in strong field ionization
of molecules. In $CO_2$ it fixes the peak ionization yield at the
experimentally observed angle of $45^\circ$ between polarization direction and
the molecular axis. In $N_2$ it changes the alignment dependence of yields by
up to a factor of 2. The effect appears on the Hartree-Fock level as well as in
full {\it ab initio} solutions of the Schr\"odinger equation.
