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.
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