  We examine the two parameter deformed superalgebra $U_{qs}(sl(1|2))$ and use
the results in the construction of quantum chain Hamiltonians. This study is
done both in the framework of the Serre presentation and in the $R$-matrix
scheme of Faddeev, Reshetikhin and Takhtajan (FRT). We show that there exists
an infinite number of Casimir operators, indexed by integers $p > 1$ in the
undeformed case and by $p \in Z$ in the deformed case, which obey quadratic
relations. The construction of the dual superalgebra of functions on
$SL_{qs}(1|2)$ is also given and higher tensor product representations are
discussed. Finally, we construct quantum chain Hamiltonians based on the
Casimir operators. In the deformed case we find two Hamiltonians which describe
deformed $t-J$ models.
