We present high-resolution, long-slit spectra of nine optically bright nuclear star-burst galaxies (SBGs) selected from the sample of Balzano from which we measure line strengths, line widths, and velocity profiles along the slit in the Hα, [N II], and [S II] emission lines. We show that these galaxies have strong nebular emission (and presumably star formation) extending over several hundred to more than a thousand parsecs from their centers. We find that the peak of the continuum and line emission profiles are displaced from the center (as defined by the rotation curve) in many of the galaxies. Gas densities and ionization levels in the SBGs fall in the range expected for giant H II region complexes, although the line widths are often much larger. The velocity profile in each galaxy is consistent with a rotation curve in which emission-line material is confined to a disk coaligned with that of the parent galaxy. The star-burst therefore likely consists of from tens to thousands of massive H II regions rather than one giant, spherical complex. The line widths would then result from an intrinsic velocity dispersion and rotational broadening.