  Using the supergravity solution of $N_1$ D3-branes probing $A_{N_2-1}$
singularities we study the pp-wave limit of $AdS_5\times S^5/Z_{N_2}$. We show
that there are two different pp-wave limits. One is the orbifold of the pp-wave
limit of $AdS_5\times S^5$. In this case there is no symmetry enhancement. The
other case is the same as the pp-wave limit of $AdS_5\times S^5$ and therefore
we again see the maximal supersymmetry. We will also identify operators in the
four dimensional ${\cal N}=2$ $SU(N_1)^{N_2}$ gauge theory which correspond to
stringy excitations in the orbifolded pp-wave geometry. The existence of the
maximal pp-wave geometry indicates that there is a subsector of the
corresponding ${\cal N}=2$ gauge theories which has enhanced ${\cal N}=4$
supersymmetry. We also study the pp-wave limits of $AdS_{7,4}\times
S^{4,7}/Z_{N}$.
