  Dissipative spin-tunneling transitions at biased resonances in molecular
magnets such as Mn-12 Ac are controlled by the dipolar field that can bring the
system on and off resonance. It is shown that this leads to spin relaxation in
form of propagating fronts of tunneling, with the dipolar field adjusting
self-consistently to provide a zero bias within the front core. There are two
regimes of the front propagation: laminar and non-laminar with discontinuous
magnetization and dipolar field. In the laminar regime the speed of the front
can exceed that of the magnetic deflagration, if the transverse field is large
enough. Fronts of tunneling can be initiated by magnetic field sweep near the
end of the crystal.
