  The subject of this paper is the derivation of the integrated Sachs-Wolfe
(iSW) effect in cosmologies with coupled dark matter and dark energy fluids.
These couplings influence the iSW-effect in three ways: The Hubble function
assumes a different scaling, the structure growth rate shows a different time
evolution, and in addition, the Poisson equation, which relates the density
perturbations to fluctuations in the gravitational potential, is changed, due
to the violation of the scaling rho ~ a^{-3} of the matter density rho with
scale factor a. Exemplarily, I derive the iSW-spectra for a model in which dark
matter decays into dark energy, investigate the influence of the dark matter
decay rate and the dark energy equation of state on the iSW-signal, and discuss
the analogies for gravitational lensing. Quite generally iSW-measurements
should reach similar accuracy in determining the dark energy equation of state
parameter and the coupling constant.
