  Various scenarios have been proposed to explain the origin of the Galactic
high-velocity clouds, predicting different distances and implying widely
varying properties for the Galaxy's gaseous halo. To eliminate the difficulties
of studying the Galactic halo from within, we have embarked on a program to
study anomalous neutral gas in external galaxies, and here we present the
results for two nearby, face-on spiral galaxies, M 83 and M 51. Significant
amounts of anomalous-velocity HI are detected in deep VLA 21-cm observations,
including an extended, slowly rotating disk and several discrete HI clouds. Our
detection algorithm reaches a limiting HI source mass of 7x10^5 solar masses,
and it allows for detailed statistical analysis of the false detection rate. We
use this to place limits on the HVC mass distributions in these galaxies and
the Milky Way; if the HVC populations are similar, then the Galactocentric HVC
distances must be less than about 25 kpc.
