  We explicitly compute the adjoint L-function of those L-packets of
representations of the group GSp(4) over a p-adic field of characteristic zero
that contain non-supercuspidal representations. As an application we verify a
conjecture of Gross-Prasad and Rallis in this case. The conjecture states that
the adjoint L-function has a pole at s=1 if and only if the L-packet contains a
generic representation.
