  Moderate deviation principles for empirical measure processes associated with
weakly interacting Markov processes are established. Two families of models are
considered: the first corresponds to a system of interacting diffusions whereas
the second describes a collection of pure jump Markov processes with a
countable state space. For both cases the moderate deviation principle is
formulated in terms of a large deviation principle (LDP), with an appropriate
speed function, for suitably centered and normalized empirical measure
processes. For the first family of models the LDP is established in the path
space of an appropriate Schwartz distribution space whereas for the second
family the LDP is proved in the space of $l_2$ (the Hilbert space of square
summable sequences)-valued paths. Proofs rely on certain variational
representations for exponential functionals of Brownian motions and Poisson
random measures.
