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The algebraic Bethe ansatz can be performed rather abstractly for wholeclasses of models sharing the same $R$-matrix, the only prerequisite being theexistence of an appropriate pseudo vacuum state. Here we perform the algebraicBethe ansatz for all models with $9 \times 9$, rational, gl(1$|$2)-invariant$R$-matrix and all three possibilities of choosing the grading. Our Betheansatz solution applies, for instance, to the supersymmetric t-J model, thesupersymmetric $U$ model and a number of interesting impurity models. It may beextended to obtain the quantum transfer matrix spectrum for this class ofmodels. The properties of a specific model enter the Bethe ansatz solution(i.e. the expression for the transfer matrix eigenvalue and the Bethe ansatzequations) through the three pseudo vacuum eigenvalues of the diagonal elementsof the monodromy matrix which in this context are called the parameters of themodel.Comment: paragraph added in section 3, reference added, version to appear in  J.Phys.

Algebraic Bethe ansatz for the gl(1|2) generalized model: II. the three gradings