  We present the results of high spatial resolution HI observations of five
intrinsically compact dwarf galaxies which are currently experiencing a strong
burst of star formation. The HI maps indicate that these systems have a complex
and clumpy interstellar medium. Unlike typical dwarf irregular galaxies, these
Blue Compact Dwarf (BCD) galaxies exhibit strong central concentrations in
their neutral gas distributions which may provide a clue to the origin of their
strong star-burst activity. Furthermore, while all of the systems do appear to
be rotating, based on observed velocity gradients, the kinematics are complex.
All systems have non-ordered kinematic structure at some level; some of the
extended gas is not necessarily kinematically connected to the main system.
  The observed gas distributions and kinematics place constraints on
evolutionary scenarios for BCDs. Evolutionary links between BCDs, dwarf
irregulars, and dwarf ellipticals have been postulated to explain their high
star formation rates and low luminosity, low metallicity nature. The BCDs
appear to have higher central mass concentrations in both gas and stellar
content than the dwarf irregulars, indicating that evolutionary scenarios
connecting these two classes will require mass redistribution. In addition, the
fact that BCDs are rotationally supported systems indicates that BCDs are
unlikely to evolve into dwarf ellipticals without substantial loss of angular
momentum. Thus, while such evolutionary scenarios may still be possible with
the aid of mergers or tidal interactions, the isolated nature of BCDs suggests
that the majority of BCDs will not fade to become objects similar to the
present day dwarf ellipticals.
