  Supersymmetric theories with a $U(1)_R$ symmetry have Dirac gauginos, solve
the supersymmetric flavor and CP problems, and have distinctive collider
signatures. However when supergravity is included, the $U(1)_R$ must be broken,
adding small Majorana mass terms which split the mass of the two components of
the Dirac gaugino and lead to oscillations between $U(1)_R$ charge eigenstates.
We present a general study of fermion-antifermion oscillations in this system,
including the effects of decays and CP violation. We consider the effects of
such oscillations in the case where the two $U(1)_R$ charge eigenstates can
decay into the same final state, and show that $O(1)$ CP violation is allowed.
In the case of decays into final states containing leptons such CP violation
can be observed as a same sign dilepton asymmetry.
