  The problem of the thermal and magnetic destruction of the critical state in
composite superconductors is investigated. The initial distributions of
temperature and electromagnetic field are assumed to be essentially
inhomogeneous. The limit of the thermomagnetic instability in quasi-stationary
approximation is determined. The obtained integral criterion, unlike the
analogous criterion for a homogeneous temperature profile, is shown to take
into account the influence of any part of the superconductor on the threshold
for critical-state instability.
