  The morphological properties of galaxies between $21 {\rm~mag} < I < 25
{\rm~mag}$ in the {\em Hubble Deep Field} are investigated using a quantitative
classification system based on measurements of the central concentration and
asymmetry of galaxian light. The class distribution of objects in the {\em
Hubble Deep Field} is strongly skewed towards highly asymmetric objects,
relative to distributions from both the {\em HST Medium Deep Survey} at $I < 22
{\rm~mag}$ and an artificially redshifted sample of local galaxies. The steeply
rising number count-magnitude relation for irregular/peculiar/merging systems
at $I < 22 {~\rm mag}$ reported in Glazebrook \etal\ (1995a) continues to at
least $I=25~{\rm mag}$. Although these peculiar systems are predominantly blue
at optical wavelengths, a significant fraction also exhibit red $U-B$ colours,
which may indicate they are at high redshift. Beyond Glazebrook \etal 's
magnitude limit the spiral counts appear to rise more steeply than
high-normalization no-evolution predictions, whereas those of elliptical/S0
galaxies only slightly exceed such predictions and may turn-over beyond $I \sim
24~{\rm mag}$. These results are compared with those from previous
investigations of faint galaxy morphology with HST and the possible
implications are briefly discussed. The large fraction of
peculiar/irregular/merging systems in the {\em Hubble Deep Field} suggests that
by $I\sim 25 {\rm~mag}$ the conventional Hubble system no longer provides an
adequate description of the morphological characteristics of a high fraction of
field galaxies.
