  We study superstring theories on the Penrose limit of the enhancon geometry
realized by the D(p+4)-branes wrapped on a K3 surface. We first examine the
null geodesics with fixed radius in general brane backgrounds, which give
solvable superstring theories with constant masses. In most cases, the
superstring theories contain negative mass-squared. We clarify a condition that
the world-sheet free fields have positive mass-squared. We then apply this
condition to the enhancon geometry and find that the null geodesics with fixed
radius exist only for p=0 case. They define the superstring theories with
positive mass-squared. For p>0 case, we show that there is no null geodesic
with fixed radius. We also discuss the decoupling limit which gives the dual
geometry of super Yang-Mills theory with 8 supercharges. We discuss the
K3-volume dependence of the superstring spectrum.
