  Microlocal analysis techniques are extended and applied to stochastic partial
differential equations (SPDEs). In particular, the H\"ormander propagation of
singularities theorem is shown to be valid for hyperbolic SPDEs driven by a
standard Brownian motion. In this case the wave front set of the solution is
invariant under the stochastic Hamiltonian flow associated to the principal
symbol of the SPDE. This study leads to the introduction of a class of random
pseudodifferential operators.
