  In this paper we are going to build the multiphoton supercoherent states for
the supersymmetric harmonic oscillator as eigenstates of the $m$-th power of a
special form (but still with a free parameter) of the Kornbluth-Zypman
supersymmetric annihilation operator. They become expressed in terms of the
multiphoton coherent states for the standard harmonic oscillator. The
Heisenberg uncertainty relation and some statistical properties for these
states will be studied. Since the multiphoton supercoherent states turn out to
be periodic, then the associated geometric phases will be as well evaluated.
