  We construct two classes of singular Kobayashi hyperbolic surfaces in $P^3$.
The first consists of generic projections of the cartesian square $V = C \times
C$ of a generic genus $g \ge 2$ curve $C$ smoothly embedded in $P^5$. These
surfaces have C-hyperbolic normalizations; we give some lower bounds for their
degrees and provide an example of degree 32. The second class of examples of
hyperbolic surfaces in $P^3$ is provided by generic projections of the
symmetric square $V' = C_2$ of a generic genus $g \ge 3$ curve $C$. The minimal
degree of these surfaces is 16, but this time the normalizations are not
C-hyperbolic.
