  The formal solution of the second order Killing tensor equations for the
general pp-wave spacetime is given. The Killing tensor equations are integrated
fully for some specific pp-wave spacetimes. In particular, the complete
solution is given for the conformally flat plane wave spacetimes and we find
that irreducible Killing tensors arise for specific classes. The maximum number
of independent irreducible Killing tensors admitted by a conformally flat plane
wave spacetime is shown to be six. It is shown that every pp-wave spacetime
that admits an homothety will admit a Killing tensor of Koutras type and, with
the exception of the singular scale-invariant plane wave spacetimes, this
Killing tensor is irreducible.
