Relaxation tests are often used in the pharmaceutical field to assess the strain rate sensitivity of pharmaceutical powders and tablets. These tests involve applying a constant strain to the powder in the die and then monitoring the stress evolution over time. Interpreting these tests is complicated because different physical phenomena, mainly viscoelasticity and viscoplasticity, occur simultaneously. These two phenomena cannot be distinguished by observing the evolution of the axial pressure alone, as it decreases in both cases. In this work, it was shown that monitoring the evolution of the die-wall pressure during relaxation can help separate the effects of these phenomena. Theoretical considerations revealed that during viscoplasticity, the die-wall pressure also decreases, whereas an increase in the die-wall pressure during relaxation indicates a viscoelastic relaxation. This was confirmed experimentally using specially designed compaction cycles on four different pharmaceutical excipients. Experimental results indicated that at low pressure, viscoplasticity was predominant, whereas at high pressure, viscoelasticity became more prominent. These results suggest that at low pressures, relaxation tests can be used to assess the viscoplastic properties of different products. However, the use of high pressure should always be avoided as viscoelastic phenomena might become more significant, and the combination of both phenomena might compromise the interpretation.