  We classify the admissible types of constraint (hermitian, holomorphic, with
reality conditions on the bosonic sectors, etc.) for generalized
supersymmetries in the presence of complex spinors. We further point out which
constrained generalized supersymmetries admit a dual formulation. For both real
and complex spinors generalized supersymmetries are constructed and classified
as dimensional reductions of supersymmetries from {\em oxidized} space-times
(i.e. the maximal space-times associated to $n$-component Clifford irreps). We
apply these results to sistematically construct a class of models describing
superparticles in presence of bosonic tensorial central charges, deriving the
consistency conditions for the existence of the action, as well as the
constrained equations of motion. Examples of these models (which, in their
twistorial formulation, describe towers of higher-spin particles) were first
introduced by Rudychev and Sezgin (for real spinors) and later by Bandos and
Lukierski (for complex spinors).
