We present high angular resolution (similar to 2 mas) radio continuum obser
vations of five Seyfert galaxies with flat-spectrum radio nuclei, using the
VLBA at 8.4 GHz. The goal of the project is to test whether these flat-spe
ctrum cores represent thermal emission from the accretion disk, as inferred
previously by Gallimore et al, for NGC 1068, or nonthermal, synchrotron se
lf-absorbed emission, which is believed to be responsible for more powerful
, flat-spectrum nuclear sources in radio galaxies and quasars. In four sour
ces (T0109-383, NGC 2110, NGC 5252, and Mrk 926), the nuclear source is det
ected but unresolved by the VLBA, indicating brightness temperatures in exc
ess of 10(8) K and sizes, on average, less than 1 pc. We argue that the rad
io emission is nonthermal and synchrotron self-absorbed in these galaxies,
but Doppler boosting by relativistic outflows is not required. Synchrotron
self-absorption brightness temperatures suggest intrinsic source sizes smal
ler than similar to 0.05-0.2 pc, for these four galaxies, the smallest of w
hich corresponds to a light-crossing time of similar to 60 light days or 10
(4) gravitational radii for a 108 hi, black hole. In one of these galaxies
(NGC 2110), there is also extended (similar to 0.2 pc) radio emission along
the same direction as the 400 pc scale jet seen with the VLA, suggesting t
hat the extended emission tomes from the base of the jet. In another galaxy
(NGC 4388), the flat-spectrum nuclear source is undetected by the VLBA. We
also present MERLIN and VLA observations of this galaxy and argue that the
observed, flat-spectrum, nuclear radio emission represents optically thin,
free-free radiation from dense thermal gas on scales similar or equal to 0
.4 to a few pc. It is notable that the two Seyfert galaxies with detected t
hermal nuclear radio emission (NGC 1068 and NGC 4388) both have large X-ray
absorbing columns, suggesting that columns in excess of similar or equal t
o 10(24) cm(-2) are needed for such disks to be detectable.