  We investigate the phenomenology of minimal four-family MSSM supergravity
theories containing an additional generation of heavy fermions along with their
superpartners. We demand: gauge coupling constant unification at high energy
scales; perturbative values for all Yukawa couplings for energy scales $\leq
\mgut$; radiative electroweak symmetry breaking via renormalization group
evolution; and a neutral LSP. The perturbative constraints imply a light
fourth-family quark and lepton spectrum, and $\tanb\lsim 3$. The lightest
CP-even Higgs mass is increased. Fourth-family Yukawa coupling contributions to
the evolution of scalar masses lead to unexpected mass hierarchies; \eg\ the
$\staupone$ is generally the lightest slepton and the lightest squark is the
$\wt\bpr_1$. A significant lower bound is placed on the gluino mass by the
requirement that the $\staupone$ not be the LSP. Sleptons of the first two
families are much more massive compared to the LSP and other neutralinos and
charginos than in the three-family models, and could easily lie beyond the
reach of a $\sqrt s=500\gev$ $\epem$ collider. Relations between slepton masses
and gaugino masses are shown to be very sensitive to the presence of a fourth
generation. The most important near-future experimental probes of the
four-family models are reviewed. A scenario with $\mt\sim\mw$ and $t\rta {\wt
t_1}\cnone$ is shown to be inconsistent with universal soft-SUSY-breaking
boundary conditions. Full four-family evolution of $\alpha_s$ is shown to lead
to a significant enhancement in inclusive jet and di-jet spectra at Tevatron
energies when all sparticle masses are near their lower bounds.
