  A supersymmetric theory in the temporal domain is constructed for bi-spinor
fields satisfying the Dirac equation. It is shown that using the Dirac matrices
basis, it is possible to construct a simple time-domain supersymmetry for
fermion fields with time-dependent mass. This theory is equivalent to a bosonic
supersymmetric theory in the time-domain. Solutions are presented, and it is
shown that they produce probability oscillations between its spinor mass
states. This theory is applied to the two-neutrino oscillation problem, showing
that the flavour state oscillations emerge from the supersymmetry originated by
the time-dependence of the unique mass of the neutrino. It is shown that the
usual result for the two-neutrino oscillation problem is recovered in the
short-time limit of this theory. Finally, it is discussed that this time-domain
fermionic supersymmetric theory cannot be obtained in the Majorana matrices
basis, thus giving hints on the Dirac fermion nature of neutrinos.
