  We formulate the stochastic dynamics of a particle subject to internal
non-white (coloured) noise in terms of path-integrals. In the simplest case,
where the noise is exponentially correlated, the weak-noise limit is
characterised by optimum paths which are given by third order differential
equations. In contrast to systems subject to white noise or external coloured
noise, the overdamped limit for these systems is singular. We analyse the
origin of this behaviour. The whole formalism is generalised to more general
noise processes and the essential features are shown to be similar to the
exponentially correlated case.
