  We show that a dynamical supersymmetry can appear in a purely fermionic
system. This ``supersymmetry without bosons" is constructed by application of a
recently introduced boson-fermion Dyson mapping from a fermion space to a space
comprised of collective bosons and ideal fermions. In some algebraic fermion
models of nuclear structure, particular Hamiltonians may lead to collective
spectra of even and odd nuclei that can be unified using the dynamical
supersymmetry concept with Pauli correlations exactly taken into account.
