Rb3H(SeO4)(2) single crystal undergoes a transition from low-temperature ferroelastic phase to superionic, paraelastic one at T-S=456 K. The low-temperature monoclinic structure contains a zero-dimensional hydrogen bond network. Above T-S, the reorienting HSeO4 groups form a dynamic hydrogen bond network in the (001) plane. The presented results of proton conductivity, ferroelastic domain pattern and differential scanning calorimeuy (DSC) studies in the vicinity of T-S show that the transition region is stretched into similar to 10 K and the transition process proceeds in steps: the changes in the ferroelastic domain pattern close to T-S are accompanied by DSC anomalies. The temperature dependence of the conductivity sigma([100]) on heating and cooling revealed similar to 2 K hysteresis of the superionic phase transition. The experimental results support the suggestion of recent papers on theoretical studies of the behaviour of protonic conductivity in M3H(XO4)(2) crystal group in the superionic phase transition region.