  We find the free field construction of the basic $W$-current and screening
currents for the deformed $W$-superalgebra ${\cal W}_{q,t}\bigl(A(M,N)\bigr)$
associated with Lie superalgebra of type $A(M,N)$. Using this free field
construction, we introduce the higher $W$-currents and obtain a closed set of
quadratic relations among them. These relations are independent of the choice
of Dynkin-diagrams for the Lie superalgebra $A(M,N)$, though the screening
currents are not. This allows us to define ${\cal W}_{q,t}\bigl(A(M,N)\bigr)$
by generators and relations.
