  We study some field representations of vector supersymmetry with superspin
Y=0 and Y=1/2 and nonvanishing central charges. For Y=0, we present two
multiplets composed of four spinor fields, two even and two odd, and we provide
a free action for them. The main differences between these two multiplets are
the way the central charge operators act and the compatibility with the
Majorana reality condition on the spinors. One of the two is related to a
previously studied spinning particle model. For Y=1/2, we present a multiplet
composed of one even scalar, one odd vector and one even selfdual two-form,
which is a truncation of a known representation of the tensor supersymmetry
algebra in Euclidean spacetime. We discuss its rotation to Minkowski spacetime
and provide a set of dynamical equations for it, which are however not derived
from a Lagrangian. We develop a superspace formalism for vector supersymmetry
with central charges and we derive our multiplets by superspace techniques.
Finally, we discuss some representations with vanishing central charges.
