  We present a large deviation principle for some stochastic evolution
equations with jumps which depend on two small parameters, when the viscosity
parameter {\epsilon} tends to zero more quickly than the homogenization's one
{\delta}{\epsilon} (written as a function of {\epsilon}). In particular, we
highlighted a large deviation principle in path-space using some classical
techniques and a uniform upper bound for the characteristic function of a
Feller process.
