Aims. We present spectroscopic observations of 182 disk galaxies (96 in the cluster and 86 in the field environment) in the region of the Abell 901/902 multiple cluster system, which is located at a redshift of z ∼ 0.165. We estimate dynamical parameters of the four subclusters and analyse the kinematics of spiral galaxies, searching for indications of ram-pressure stripping. Furthermore, we focus on dusty red galaxies as a possible intermediate stage in the transformation of field galaxies to lenticulars when falling into the cluster. Methods. We obtained multi-object slit spectroscopy using the VLT instrument VIMOS. We carried out a redshift analysis, determined velocity dispersions using biweight statistics, and detected possible substructures with the Dressler-Shectman test. We exploited rotation curves from emission lines to analyse distortions in the gaseous disk of a galaxy, as well as HST/ACS images to quantify the morphological distortions of the stellar disk. Results. The presence of substructures and non-Gaussian redshift distributions indicate that the cluster system is dynamically young and not in a virialised state. We find evidence of two important galaxy populations. Morphologically distorted galaxies are probably subject to increased tidal interactions. They show pronounced rotation-curve asymmetries at intermediate cluster-centric radii and low rest-frame peculiar velocities. Morphologically undistorted galaxies show the strongest rotation-curve asymmetries at high rest-frame velocities and low cluster-centric radii. Supposedly, this group is strongly affected by ram-pressure stripping due to interaction with the intra-cluster medium. Among the morphologically undistorted galaxies, dusty red galaxies have particularly strong rotation-curve asymmetries, suggesting that ram pressure is an important factor in these galaxies. Furthermore, dusty red galaxies have on average a bulge-to-total ratio that is higher by a factor of two than cluster blue-cloud and field galaxies. The fraction of kinematically distorted galaxies is 75% higher in the cluster than in the field environment. This difference mainly stems from morphologically undistorted galaxies, indicating a cluster-specific interaction process that only affects the gas kinematics but not the stellar morphology. Also the ratio between gas and stellar scale length is reduced for cluster galaxies compared to the field sample. Both findings could be explained best by ram-pressure effects. Conclusions. Ram-pressure stripping seems to be an important interaction process in the multiple cluster system A901/902. Dusty red galaxies might be a crucial element in understanding the transformation of field disk galaxies into cluster lenticular galaxies.