  A natural non-Markovian extension of the theory of white noise quantum
trajectories is presented. In order to introduce memory effects in the
formalism an Ornstein-Uhlenbeck coloured noise is considered as the output
driving process. Under certain conditions a random Hamiltonian evolution is
recovered. Moreover, non-Markovian stochastic Schr\"odinger equations which
unravel non-Markovian master equations are derived.
