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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   $\mathfrak {gl}(M,N)$  .

RTT Realization of Quantum Affine Superalgebras and Tensor Products