  We present detailed modeling of periodic flaring events in the 6.7 GHz and
12.2 GHz methanol lines as well as the OH 1665 MHz and 1667 MHz transitions
observed in the G9.62+0.20E star-forming region. Our analysis is performed
within the framework of the one-dimensional Maxwell-Bloch equations, which
intrinsically cover the complementary quasi-steady state maser and transient
superradiance regimes. We find that the variations in flaring time-scales
measured for the different species/transitions, and sometimes even for a single
spectral line, are manifestations of and are best modeled with Dicke's
superradiance, which naturally accounts for a modulation in the duration of
flares through corresponding changes in the inversion pump. In particular, it
can explain the peculiar behaviour observed for some features, such as the
previously published result for the OH 1667 MHz transition at
$v_\mathrm{lsr}=+1.7$ km s$^{-1}$ as well as the methanol 6.7 GHz line at
$v_\mathrm{lsr}=-1.8$ km s$^{-1}$, through a partial quenching of the
population inversion during flaring events.
