  For the gauge massless higher spin 4D, N = 1 off-shell supermultiplets
previously developed, we provide evidence of a twistor-like oscillator
realization that is intrinsically related to the superfield structure of the
dynamical variables and gauge transformations. Gauge invariant field strengths
and linearized Bianchi identities for these multiplets are worked out. It is
further argued, inspired by earlier non- supersymmetric constructions due to
Klishevich and Zinoviev, that a massive superspin-$s$ multiplet can be
described as a gauge-invariant dynamical system involving massless multiplets
of superspins s, s-1/2, ..., 0. A gauge-invariant formulation for the massive
gravitino multiplet is discussed in some detail.
