  The purpose of this paper is twofold. The first is to apply the method
introduced in the works of Nakayashiki and Smirnov on the Mumford system to its
variants. The other is to establish a relation between the Mumford system and
the isospectral limit $\mathcal{Q}_g^{(I)}$ and $\mathcal{Q}_g^{(II)}$ of the
Noumi-Yamada system. As a consequence, we prove the algebraically completely
integrability of the systems $\mathcal{Q}_g^{(I)}$ and $\mathcal{Q}_g^{(II)}$,
and get explicit descriptions of their solutions.
