Extended X-ray absorption fine structure (EXAFS) and neutron diffraction experiments were carried out to clarify the typical features of the local structure of a family of medium-entropy alloys (CrCoNi, MnCoNi, and FeCoNi). A simple random cluster model was constructed for analyzing EXAFS spectra, and static and dynamic components of the mean-square relative displacement (MSRD) were separately extracted. In our analysis, the static MSRD of the MnCoNi sample was slightly larger than those of the CrCoNi and FeCoNi samples, whereas the dynamic MSRDs of these samples were almost identical. Based on the complementary neutron diffraction data, we argued that the origin of the large static displacement in the MnCoNi alloy can be associated with a short-range structural transformation through long-term structural relaxation.