  We measure quantitative structural parameters of galaxies in the Hubble Deep
Field (HDF) on the drizzled F814W images. Our structural parameters are based
on a two-component surface brightness made up of a S\'ersic profile and an
exponential profile. We compare our results to the visual classification of van
den Bergh et al. (1996) and the $C-A$ classification of Abraham et al. (1996a).
Our morphological analysis of the galaxies in the HDF indicates that the
spheroidal galaxies, defined here as galaxies with a dominant bulge profile,
make up for only a small fraction, namely 8% of the galaxy population down to
m$_{F814W}(AB)$ = 26.0. We show that the larger fraction of early-type systems
in the van den Bergh sample is primarily due to the difference in
classification of 40% of small round galaxies with half-light radii <
0\arcsecpoint 31. Although these objects are visually classified as elliptical
galaxies, we find that they are disk-dominated with bulge fractions < 0.5.
Given the existing large dataset of HDF galaxies with measured spectroscopic
redshifts, we are able to determine that the majority of distant galaxies
($z>2$) from this sample are disk-dominated. Our analysis reveals a subset of
HDF galaxies which have profiles flatter than a pure exponential profile.
