We study the Nonlinear (Polynomial, N-fold, . . . ) SUSY 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 Super-Hamiltonian if supercharges represent differential operators of finite order. The appearance of the extended SUSY with several supercharges is analyzed and it is established that no more than two independent supercharges may generate a nonlinear superalgebra. In the case with two independent supercharges we find a nontrivial hidden symmetry operator. It is revealed that wave functions of all Super-Hamiltonian bound states or, in the case of Super-Hamiltonian with periodic potential(s), all periodic wave functions corresponding to boundaries between allowed and forbidden energy bands are zero-modes of the hidden symmetry op