  Since the heavy neutrinos of the inverse seesaw mechanism mix largely with
the standard ones, the charged currents formed with them and the muons have the
potential of generating robust and positive contribution to the anomalous
magnetic moment of the muon. Ho\-we\-ver, bounds from the non-unitary in the
leptonic mixing matrix may restrict so severely the parameters of the mechanism
that, depending on the framework under which the mechanism is implemented, may
render it unable to explain the recent muon g-2 result. In this paper we show
that this happens when we implement the mechanism into the standard model and
into two versions of the 3-3-1 models.
