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 Sersic 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 < 0arcsecpoint 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.
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