  We introduce two algebraic completely integrable analogues of the Mumford
systems which we call hyperelliptic Prym systems, because every hyperelliptic
Prym variety appears as a fiber of their momentum map. As an application we
show that the generic fiber of the momentum map of the periodic Volterra
lattice $$\dot a_i=a_i(a_{i-1}-a_{i+1}), \qquad i=1,...,n,\quad a_{n+1}=a_1,$$
is an affine part of a hyperelliptic Prym variety, obtained by removing $n$
translates of the theta divisor, and we conclude that this integrable system is
algebraic completely integrable.
