Recent systematic studies of the basic properties of type SRa and SRb Semiregular variables (SRVs) have found that the SRbs consist of a "blue" group with no circumstellar shells, short periods and higher temperatures and a "red" group with temperatures and mass loss rates comparable to Miras but periods about a factor of two smaller. Near IR photometry shows that the "blue" SRVs are similar to non-variable giants, while the "red" SRVs are intermediate objects between Miras and normal giants. The difference in atmospheric structure, most prominently seen in the strength of the water bands, could be due to the smaller pulsation amplitudes and weaker shockfronts of the SRVs. Thus, when compared to Miras and non-variable giants, the "red" SRVs can provide important clues for the influence of the pulsational behaviour on the atmospheric structure and mass loss of AGB stars. Many of the theoretical tools for interpreting the spectra of these stars are available now. Since no detailed spectroscopic studies in the IR exist, we propose to obtain SWS spectra of selected "red" SRVs. These will be compared with state of the art theoretical models. The SWS on board of ISO covers most of the important molecular bands of H2O, CO and SiO and the wavelength region where continuous dust emission starts to dominate. While some of the mentioned bands can be observed from the ground, this requires different instruments and often excellent observing conditions. The use of different instruments generally means that different molecular bands and the dust emission cannot be studied at the same time, a severe disadvantage in view of the variability of AGB stars and the pronounced coupling between dust and different molecules. Only ISO can provide, probably for a long time, complete, simultaneous and homogeneous data of the molecular bands and the dust emission.