  We discuss dynamical response theory of driven-dissipative quantum systems
described by Markovian Master Equations generating semi-groups of maps. In this
setting thermal equilibrium states are replaced by non-equilibrium steady
states and dissipative perturbations are considered besides the Hamiltonian
ones. We derive explicit expressions for the linear dynamical response
functions for generalized dephasing channels and for Davies thermalizing
generators. We introduce the notion of maximal harmonic response and compute it
exactly for a single qubit channel. Finally, we analyze linear response near
dynamical phase transitions in quasi-free open quantum systems. It is found
that the effect of the dynamical phase transition shows up in a peak at the
edge of the spectrum in the imaginary part of the dynamical response function.
