The longitudinal relaxation of interacting spins is studied under the
influence of a strong external magnetic field exceeding the scale of t
he interaction. Nonadiabatic spin flips involving multispin processes
which compensate the large Zeeman splitting energy are considered with
in the frame of a one dimensional X-Y model. An extended scheme of non
-resonant phononless flip-flop transitions is applied to spin relaxati
on in a crystal consisting of magnetic molecules Mn12O12 with acetate
ions. It is shown that unusual features in the magnetic field dependen
ce of the relaxation rate can be accounted for by a crude generalizati
on of the X-Y model to three dimensions.