  The stability of superconducting films with respect to oscillatory precursor
modes for thermomag- netic avalanches is investigated theoretically. The
results for the onset threshold show that previous treatments of
non-oscillatory modes have predicted much higher thresholds. Thus, in film
supercon- ductors, oscillatory modes are far more likely to cause
thermomagnetic breakdown. This explains the experimental fact that flux
avalanches in film superconductors can occur even at very small ramping rates
of the applied magnetic field. Closed expressions for the threshold magnetic
field and temperature, as well oscillation frequency, are derived for different
regimes of the oscillatory thermomagnetic instability.
