Simultaneous tunneling of an electron and nuclei    
in hydrogen bonded molecular clusters 
which support a dipole bound electron is reported.  A whole class of systems including
hydrogen halide and water dimer anions 
is predicted to exhibit this effect. A measurable signature of
double tunneling is a strong reduction of the tunneling splitting
compared to the neutral cluster. Quantum mechanical calculations
give for the hydrogen fluoride dimer anion a ground state tunneling splitting of 114 MHz,
while for the first excited vibrational state the tunneling splitting reaches 4.20 GHz.