  We present a theoretical study of atom - molecule collisions in superimposed
electric and magnetic fields and show that dynamics of electronic spin
relaxation in molecules at temperatures below 0.5 K can be manipulated by
varying the strength and the relative orientation of the applied fields. The
mechanism of electric field control of Zeeman transitions is based on an
intricate interplay between intramolecular spin-rotation couplings and
molecule-field interactions. We suggest that electric fields may affect
chemical reactions through inducing nonadiabatic spin transitions and
facilitate evaporative cooling of molecules in a magnetic trap.
