  We develop an Onsager-Machlup-type theory for nonequilibrium semi-Markov
processes. Our main result is an exact large time asymptotics for the joint
probability of the occupation times and the currents in the system,
establishing some generic large deviation structures. We discuss in detail how
the nonequilibrium driving and the non-exponential waiting time distribution
influence the occupation-current statistics. The violation of the Markov
condition is reflected in the emergence of a new type of nonlocality in the
fluctuations. Explicit solutions are obtained for some examples of driven
random walks on the ring.
