  The fluctuations of a Markovian jump process with one or more unidirectional
transitions, where $R_{ij} >0$ but $R_{ji} =0$, are studied. We find that such
systems satisfy an integral fluctuation theorem. The fluctuating quantity
satisfying the theorem is a sum of the entropy produced in the bidirectional
transitions and a dynamical contribution which depends on the residence times
in the states connected by the unidirectional transitions. The convergence of
the integral fluctuation theorem is studied numerically, and found to show the
same qualitative features as in systems exhibiting microreversibility.
