A detailed theoretical analysis of the resonant macroscopic quantum tu
nneling in superconducting quantum interference device systems is pres
ented. Our approach allows us to include the effect of both temperatur
e and sweeping rate of the external flux, and to study the phenomenon
both in quasistationary and nonstationary conditions, which can be ind
uced by a fast sweep of the external bias. Moreover we compare our the
ory with the experimental data of Rouse, Han, and Lukens [Phys. Rev. L
ett. 75, 1614 (1995)] referring to the quasi-stationary case, while ot
her observable effects are predicted in the nonstationary case.