  Nonlinear supercoherent states, which are eigenstates of nonlinear
deformations of the Kornbluth-Zypman annihilation operator for the
supersymmetric harmonic oscillator, will be studied. They turn out to be
expressed in terms of nonlinear coherent states, associated to the
corresponding deformations of the standard annihilation operator. We will
discuss as well the Heisenberg uncertainty relation for a special particular
case, in order to compare our results with those obtained for the
Kornbluth-Zypman linear supercoherent states. As the supersymmetric harmonic
oscillator executes an evolution loop, such that the evolution operator becomes
the identity at a certain time, thus the linear and nonlinear supercoherent
states turn out to be cyclic and the corresponding geometric phases will be
evaluated.
