  We have studied the relation between HI linewidth and optical luminosity in
two samples of dwarf galaxies, with special attention to the accuracy of the
inclination correction. The first sample consists of rotationally supported
galaxies, and has DDO 154 as a prototype. They have HI linewidths significantly
larger than predicted by an extrapolation of the Tully-Fisher relation. The
deviation from the extrapolated Tully-Fisher relation correlates with the
distance-independent mass-to-luminosity ratio M_HI/L_B. The baryonic correction
for these gas rich galaxies is too small to explain the deviation from the
Tully-Fisher relation, unless a small mass-to-light ratio (M/L_B)_* <= 0.25 for
the stellar population is assumed. The second sample contains dwarf galaxies
with comparable rotational and random velocities. This sample, having Leo A as
a prototype, is consistent with an extrapolation of the classical Tully-Fisher
relation to lower luminosities. These dwarf galaxies are not particularly rich
in gas, but their mass is dominated by baryonic matter within their HI radius.
We suggest that any evolution of the deviating galaxies towards the
Tully-Fisher relation will combine a decrease in linewidth by radial transport
of HI with an increase in luminosity due to a larger accumulated stellar mass.
