  The fluctuation-dissipation relation is calculated for a class of stochastic
models obeying a master equation. The transition rates are assumed to obey
detailed balance also in the presence of a field. It is shown that in general
the linear response cannot be expressed via time-derivatives of the correlation
function alone, but an additional function $\xi(t,t_w)$, which has been rarely
discussed before is required. This function depends on the two times also
relevant for the response and the correlation and vanishes under equilibrium
conditions. It can be expressed in terms of the propagators and the transition
rates of the master equation but it is not related to any physical observable
in an obvious way. Instead, it is determined by inhomogeneities in the temporal
evolution of the distribution function of the stochastic variable under
consideration. $\xi(t,t_w)$ is considered for some examples of stochastic
models, some of which exhibit true non-equilibrium dynamics and others approach
equilibrium in the long term. In particular, models in which a relevant
variable, e.g. a magnetization, is related in a prescribed way to the states of
the system are considered as projections from a composite Markov process. From
these model calculations, it is conjectured that $\xi(t,t_w)$ vanishes when one
is concerned with measurements of the analogue of a structure factor for large
wave-vectors or if every transition among the states randomizes the value of
the stochastic variable considered.
