  We use the RTT realization of the quantum affine superalgebra associated with
the Lie superalgebra $\mathfrak{gl}(M,N)$ to study its finite-dimensional
representations and their tensor products. In the case $\mathfrak{gl}(1,1)$,
the cyclicity condition of tensor products of finite-dimensional simple modules
is determined completely in terms of zeros and poles of rational functions.
This in turn induces cyclicity of some particular tensor products of
Kirillov-Reshetikhin modules related to $\mathfrak{gl}(M,N)$.
