  We have made observations of the \ion{H}{1} in the southern ringed barred
spiral galaxies NGC~1433 and NGC~6300 with the Australia Telescope Compact
Array (ATCA), the main goal being to test the resonance theory for the origin
of these rings. NGC~1433 is the prototypical ringed barred spiral, and displays
distinct \ion{H}{1}~counterparts to its nuclear ring, inner ring, outer
pseudoring, and plume-like features. The $L_{4}$ and $L_{5}$ regions at
corotation, as well as the bar itself, are relatively devoid of neutral atomic
hydrogen. By associating the inner ring of NGC~1433 with the inner second
harmonic resonance, and its outer pseudoring with the outer Lindblad resonance,
we are able to infer a bar pattern speed for NGC~1433 of
$26\pm5$~km~s$^{-1}$~kpc$^{-1}$. By way of contrast, NGC~6300 possesses a much
more extended \ion{H}{1}~disk than NGC~1433. There is a gas ring underlying the
inner pseudoring, but it is both broader and slightly larger in diameter than
the optical feature. By again linking this inner ring feature to the inner
second harmonic resonance, we derive a bar pattern speed for NGC~6300 of
$27\pm8$~km~s$^{-1}$~kpc$^{-1}$, but in this case, neither the outer pseudoring
nor the nuclear ring predicted by the resonance-ring theory can be identified
in NGC~6300. Although it may be the case that the ring in NGC~6300 is not
related to a resonance with the bar at all, we postulate instead that NGC~6300
is merely a less well-developed example of a resonance-ring galaxy than is
NGC~1433.
