  For a given hyperelliptic curve $C$ over a finite field with Jacobian $J_C$,
we consider the hyperelliptic analogue of the congruential generator defined by
$W_n=W_{n-1}+D$ for $n\geq 1$ and $D,W_0\in J_C$. We show that curves of genus
2 produce sequences with large linear complexity.
