In this paper we consider the interaction of a quantum-mechanical supe
rconducting quantum interference device (SQUID) with a classical monoc
hromatic electromagnetic (EM) field. We solve the time-dependent Schro
dinger equation for the SQUID ring in this EM field. We demonstrate th
at nonperturbative transitions between the low-lying states of the rin
g, due to coherent multiphoton absorption processes, dominate, even wh
en the single-photon energy is small compared with the energy separati
on between these states. We present experimental data on small-capacit
ance SQUID rings, interacting with microwave fields, which point to th
e existence of such nonperturbative transitions.