  We present a detailed morphological analysis of the galaxy populations in the
first two clusters to be completed in an extensive observational study of nine
high-redshift clusters of galaxies (Oke, Postman & Lubin 1998). These two
clusters, CL0023+0423 and CL1604+4304, are at redshifts of z = 0.84 and z =
0.90, respectively. The morphological studies are based on high-angular
resolution imagery taken with WFPC2 aboard the Hubble Space Telescope. These
data are combined with deep, ground-based BVRI photometry and spectra taken
with the Keck 10-meter telescopes. Based on these observations, CL0023+0423 has
a galaxy population which is more similar to groups of galaxies and the field.
This system is almost completely dominated by spiral galaxies. CL1604+4304,
however, has a morphological composition which is more typical of a normal,
present-day cluster; early-type galaxies comprise approximately 76% of all
galaxies brighter than M_V = -19.0 + 5 log h in the central 0.5 h^{-1} Mpc. The
ratio of S0 galaxies to ellipticals in this cluster is 1.7 +/- 0.9, consistent
with local cluster populations. The morphological results support the
conclusions of the dynamical analysis presented in the second paper of this
series (Postman, Lubin & Oke 1998). CL0023+0423 consists of two galaxy groups
which are separated by approximately 2900 km/s in radial velocity. On the other
hand, CL1604+4304 has a morphological composition, velocity dispersion, and
implied mass which are consistent with an Abell richness class 2 or 3 cluster.
