The extension of the surface hopping method ''molecular dynamics with quantum transitions'' (MDQT) to double proton transfer and proton-coupled electron transfer reactions is tested by comparison to fully quantum dynamical calculations for simple model systems. These model systems each include four potential energy surfaces and three or four avoided curve crossings. The agreement between the MDQT and fully quantum dynamical calculations provides validation for the application of MDQT to these biologically important processes. (C) 1997 American Institute of Physics.