Nonsteroidal anti-inflammatory drugs (NSAIDs) are widely prescribed for their antipyretic, anti-inflammatory, and painkiller actions despite a wide spectrum of side effects. The mechanisms involved in their therapeutic actions and side-effects have not been clearly understood yet. The assertion that effects of NSAIDs are related to their action at cellular membrane level has stimulated the investigation of interaction between NSAIDs and membranes. Here, we report effects of two different NSAIDs, ibuprofen and indomethacin, on the thermotropic phase behaviour and the dynamics of DMPC membrane as studied using neutron scattering techniques. Elastic intensity scan measurements showed that both drugs substantially alter the phase behaviour of the membrane. However, the effects of these drugs are found to differ quantitatively, which is correlated with their respective interactions with phospholipid membrane. Quasielastic neutron scattering measurements showed that in the ordered phase, both drugs enhance the dynamics of the membrane, but the drugs' effects on the membrane dynamics differ in the fluid phase. Indomethacin suppresses the dynamics of the membrane, whereas ibuprofen does not show significant effect at the same molar concentration. We have also investigated the effect of concentration of ibuprofen on the dynamics of the membrane. Our measurements provide clear evidence that interaction of NSAID with the membrane depends on both the physical state of the membrane and the nature and concentration of NSAID. Hence, one must investigate each NSAID independently while analysing its action mechanism. Better understanding of NSAID-membrane interaction can pave the way for designing more effective NSAID with reduced side effects. Display omitted •Effects of ibuprofen and indomethacin on motions of the membrane lipids are probed.•NSAID-membrane interaction depends on membrane phase state and drug concentration.•NSAIDs broaden the main phase transition and shift it towards a lower temperature.•In ordered phase, ibuprofen and indomethacin enhance the dynamics of the membrane.•In fluid phase, indomethacin, but not ibuprofen, suppresses the membrane dynamics.