  The mean electromotive force caused by turbulence of an electrically
conducting fluid, which plays a central part in mean--field electrodynamics, is
calculated for a rotating fluid. Going beyond most of the investigations on
this topic, an additional mean motion in the rotating frame is taken into
account. One motivation for our investigation originates from a planned
laboratory experiment with a Ponomarenko-like dynamo. In view of this
application the second--order correlation approximation is used. The
investigation is of high interest in astrophysical context, too. Some
contributions to the mean electromotive are revealed which have not been
considered so far, in particular contributions to the $\alpha$--effect and
related effects due to the gradient of the mean velocity. Their relevance for
dynamo processes is discussed. In a forthcoming paper the results reported here
will be specified to the situation in the laboratory and partially compared
with experimental findings.
