  We formulate a multi-band generalisation of the time-dependent Gutzwiller
theory. This approach allows for the calculation of general two-particle
response functions, which are crucial for an understanding of various
experiments in solid-state physics. As a first application, we study the
momentum- and frequency-resolved magnetic susceptibility in a two-band Hubbard
model. Like in the underlying ground-state approaches we find significant
differences between the results of our method and those from a time-dependent
Hartree-Fock approximation.
