  The quantum regression theorem is a powerful tool for calculating the
muli-time correlators of operators of open quantum systems which dynamics can
be described in Markovian approximation. It enables to obtain the closed system
of equation for the multi-time correlators. However, the scope of the quantum
regression theorem is limited by a particular time order of the operators in
multi-time correlators and does not include out-of-time-ordered correlators. In
this work, we obtain an adjoint master equation for multi-time correlators that
is applicable to out-of-time-ordered correlators. We show that this equation
can be derived for various approaches to description of the dynamics of open
quantum systems, such as the global or local approach. We show that the adjoint
master equation for multi-time correlators is self-consistent. Namely, the
final equation does not depend on how the operators are grouped inside the
correlator, and it coincides with the quantum regression theorem for the
particular time ordering of the operators.
