  We present an exact treatment of the hysteresis behavior of the
zero-temperature random-field Ising model on a Bethe lattice when it is driven
by an external field and evolved according to a 2-spin-flip dynamics. We focus
on lattice connectivities z=2 (the one-dimensional chain) and z=3. For the
latter case, we demonstrate the existence of an out-of-equilibrium phase
transition, in contrast with the situation found with the standard 1-spin-flip
dynamics. We discuss the influence of the degree of cooperativity of the
(local) spin dynamics of the nonequilibrium response on the system.
