Photoinduced absorption in nanostructures with doped Ge/Si quantum dots as well as in undoped structures, was studied. Spectra of photoinduced absorption at cryogenic temperatures under direct and indirect in real space  resonant interband pumping, as well as time-resolved spectra were obtained. Two high-energy peaks detected in the absorption spectra may be associated with intraband hole transitions from the ground and excited states of  quantum dots to the continuous spectrum. The low-energy peak corresponds to interlevel transitions of holes between the ground and excited states. The dynamics of the decay of high-energy peaks can be described in terms of fast and slow components associated with the capture of photoexcited carriers on the levels in a quantum dot. Structures with Ge/Si quantum dots can be used to develop mid-infrared detectors.