  This article treats long term average impulse control problems with running
costs in the case that the underlying process is a L\'evy process. Under quite
general conditions we characterize the value of the control problem as the
value of a stopping problem and construct an optimal strategy of the control
problem out of an optimizer of the stopping problem if the latter exists.
Assuming a maximum representation for the payoff function, we give easy to
verify conditions for the control problem to have an $\left(s,S\right)$
strategy as an optimizer. The occurring thresholds are given by the roots of an
explicit auxiliary function. This leads to a step by step solution technique
whose utility we demonstrate by solving a variety of examples of impulse
control problems.
