In this study we investigate the rate-dependency of the mechanical behaviour of semilunar heart valves under biaxial deformation, from quasi-static to physiological loading rates. This work extends and complements our previous undertaking, where the rate-dependency in the mechanical behaviour of semilunar valve specimens was documented in sub-physiological rate domains (Acta Biomater. 2019, https://doi.org/10.1016/j.actbio.2019.02.008). For the first time we demonstrate herein that the stress-stretch curves obtained from specimens under physiological rates too are markedly different to those at sufficiently lower rates and at quasi-static conditions. The results importantly underline that the mechanical behaviour of semilunar heart valves is rate dependent, and the physiological mechanical behaviour of the valves may not be correctly obtained via material characterisation tests at arbitrary low deformation rates. Presented results in this work provide an inclusive dataset for material characterisation and modelling of semilunar heart valves across a 10,000 fold deformation rate, both under equi-biaxial and 1:3 ratio deformation rates. The important application of these results is to inform the development of appropriate mechanical testing protocols, as well as devising new models, for suitable determination of the rate-dependent constitutive mechanical behaviour of the semilunar valves.