  While Wigner functions forming phase space representation of quantum states
is a well-known fact, their construction for noncommutative quantum mechanics
(NCQM) remains relatively lesser known, in particular with respect to gauge
dependencies. This paper deals with the construction of Wigner functions of
NCQM for a system of 2-degrees of freedom using 2-parameter families of gauge
equivalence classes of unitary irreducible representations (UIRs) of the Lie
group $\g$ which has been identified as the kinematical symmetry group of NCQM
in an earlier paper. This general construction of Wigner functions for NCQM, in
turn, yields the special cases of Landau and symmetric gauges of NCQM.
