Investigations of transient two-phase flow oscillations in single channels and monolithic catalyst supports are described. The experimental investigations were conducted in glass capillaries of varying inner diameter as well as ceramic monoliths. As a result of the experimental investigations pressure drop instabilities were found both in reference to the liquid and the gaseous phase, When coupling the test sections with compressible volumes in the feedlines of the phases pressure drop oscillations of the two-phase flow are established. A model is presented for the theoretical description of the resulting transient how oscillations. The basis for the model are the momentum and mass conservation equations for all the components. For the flow instability developing in the test section experimental results are used, The non-linear differential equations of second order are solved by a dynamic finite step numerical scheme. The experimental and the theoretical results for the pressure drop oscillations are compared.