  Using the Morse-theoretic techniques introduced by Hitchin, we prove that the
moduli space of $\Sp(2p,2q)$-Higgs bundles over a compact Riemann surface of
genus $g\geq 2$ is connected. In particular, this implies that the moduli space
of representations of the fundamental group of the surface in $\Sp(2p,2q)$ is
connected.
