  We present an extensive search for a general class of flipped $SU(5)$ models
built within the free fermionic formulation of the heterotic string. We
describe a set of algorithms which constitute the basis for a computer program
capable of generating systematically the massless spectrum and the
superpotential of all possible models within the class we consider. Our search
through the huge parameter space to be explored is simplified considerably by
the constraint of $N=1$ spacetime supersymmetry and the need for extra $Q,\bar
Q$ representations beyond the standard ones in order to possibly achieve string
gauge coupling unification at scales of ${\cal O}(10^{18}\GeV)$. Our results
are remarkably simple and evidence the large degree of redundancy in this kind
of constructions. We find one model with gauge group $SU(5)\times
U(1)_\ty\times SO(10)_h\times SU(4)_h\times U(1)^5$ and fairly acceptable
phenomenological properties. We study the $D$- and $F$-flatness constraints and
the symmetry breaking pattern in this model and conclude that string gauge
coupling unification is quite possible.
