Thermoplastic elastomer vulcanizate (TPV) and liquid silicone rubber (LSR) are replacement candidates for ethylene-propylene-diene rubbers (EPDM), as they offer the possibility for two-component injection moulding. In this study, these material types were compared side by side in cyclic compression tests. The materials were also characterized to provide details on the formulations. Compared to the rubbers, the TPV had higher compression set (after a given cycle) and hysteresis loss, and a stronger Mullins effect. This is due to the thermoplastic matrix in the TPV. The LSR had lower compression set (after a given cycle) than the EPDM, but stronger Mullins effect and higher relative hysteresis loss. These differences between the LSR and the EPDM are likely due to differences in polymer network structure and type of filler. Methods for quantifying the Mullins effect are proposed, and correlations between a Mullins index and parameters such as compression set are discussed. The EPDMs showed a distinct trend in compression set, relative hysteresis loss and relaxed stress fraction vs. strain amplitude; these entities were almost independent of strain amplitude in the range 15–35%, while they increased in this range for the TPV and the LSR. The difference between the compression set values of the LSR and the EPDM decreased with increasing strain amplitude and increasing strain recovery time.