  We study the Nonlinear (Polynomial, N-fold,...) Supersymmetry algebra in
one-dimensional QM. Its structure is determined by the type of conjugation
operation (Hermitian conjugation or transposition) and described with the help
of the Super-Hamiltonian projection on the zero-mode subspace of a supercharge.
We show that the SUSY algebra with transposition symmetry is always polynomial
in the Hamiltonian if supercharges represent differential operators of finite
order. The appearance of the extended SUSY with several (complex or real)
supercharges is analyzed in details and it is established that no more than two
independent supercharges may generate a Nonlinear superalgebra which can be
appropriately specified as {\cal N} = 2 SUSY. In this case we find a
non-trivial hidden symmetry operator and rephrase it as a non-linear function
of the Super-Hamiltonian on the physical state space. The full {\cal N} = 2
Non-linear SUSY algebra includes "central charges" both polynomial and
non-polynomial (due to a symmetry operator) in the Super-Hamiltonian.
