  We find the conditions under which a quantum regression theorem can be
assumed valid for non-Markovian master equations consisting in Lindblad
superoperators with memory kernels. Our considerations are based on a
generalized Born-Markov approximation, which allows us to obtain our results
from an underlying Hamiltonian description. We demonstrate that a non-Markovian
quantum regression theorem can only be granted in a stationary regime if the
dynamics satisfies a quantum detailed balance condition. As an example we study
the correlations of a two level system embedded in a complex structured
reservoir and driven by an external coherent field.
