  We have developed a quantitative theory of resonant tunneling of magnetic
flux between discrete macroscopically distinct quantum states in SQUID systems.
The theory is based on the standard density-matrix approach. Its new elements
include the discussion of the two different relaxation mechanisms that exist
for the double-well potential, and description of the ``photon-assisted''
tunneling driven by external rf radiation. It is shown that in the case of
coherent flux dynamics, rf radiation should lead to splitting of the peaks of
resonant flux tunneling, indicating that the resonant tunneling is a convenient
tool for studying macroscopic quantum coherence of flux.
