This paper describes a method to obtain state model parameters for an infinite series of Links–Gould link invariants LG, based on quantum R matrices associated with the (0̇m | α̇n) representations of the quantum superalgebras Uq [gl(m|n)]. Explicit details of the state models for the cases n = 1 and m = 1, 2, 3, 4 are supplied. Some evaluations of the new link invariants are provided, as are some...