  The existence of intimate relation between generalized statistics and
supersymmetry is established by observation of hidden supersymmetric structure
in pure parabosonic systems. This structure is characterized generally by a
nonlinear superalgebra. The nonlinear supersymmetry of parabosonic systems may
be realized, in turn, by modifying appropriately the usual supersymmetric
quantum mechanics. The relation of nonlinear parabosonic supersymmetry to the
Calogero-like models with exchange interaction and to the spin chain models
with inverse-square interaction is pointed out.
