  We show that for positive integer values $l$ of the parameter in the
conformal mechanics model the system possesses a hidden nonlinear
superconformal symmetry, in which reflection plays a role of the grading
operator. In addition to the even $so(1,2)\oplus u(1)$-generators, the
superalgebra includes $2l+1$ odd integrals, which form the pair of
spin-$(l+{1/2})$ representations of the bosonic subalgebra and anticommute for
order $2l+1$ polynomials of the even generators. This hidden symmetry, however,
is broken at the level of the states in such a way that the action of the odd
generators violates the boundary condition at the origin. In the earlier
observed double nonlinear superconformal symmetry, arising in the
superconformal mechanics for certain values of the boson-fermion coupling
constant, the higher order symmetry is of the same, broken nature.
