  In this paper we investigate trigonometric vertex models associated with
solutions of the Yang-Baxter equation which are invariant relative to
q-deformed superalgebras sl(r|2m)^(2), osp(r|2m)^(1) and osp(r=2n|2m)^(2). The
associated R-matrices are presented in terms of the standard Weyl basis making
possible the formulation of the quantum inverse scattering method for these
lattice models. This allowed us to derive the eigenvectors and the eigenvalues
of the corresponding transfer matrices as well as explicit expressions for the
Bethe ansatz equations.
