  We show that a simple change of the classical boson-fermion coupling
constant, $2\alpha \to 2\alpha n $, $n\in \N$, in the superconformal mechanics
model gives rise to a radical change of a symmetry: the modified classical and
quantum systems are characterized by the nonlinear superconformal symmetry. It
is generated by the four bosonic integrals which form the so(1,2) x u(1)
subalgebra, and by the 2(n+1) fermionic integrals constituting the two spin-n/2
so(1,2)-representations and anticommuting for the order n polynomials of the
even generators. We find that the modified quantum system with an integer value
of the parameter $\alpha$ is described simultaneously by the two nonlinear
superconformal symmetries of the orders relatively shifted in odd number. For
the original quantum model with $|\alpha|=p$, $p\in \N$, this means the
presence of the order 2p nonlinear superconformal symmetry in addition to the
osp(2|2) supersymmetry.
