Flexibility is key to survival for seaweeds exposed to the extreme hydrodynamic environment of wave-washed rocky shores. This poses a problem for coralline algae, whose calcified cell walls make them rigid. Through the course of evolution, erect coralline algae have solved this problem by incorporating joints (genicula) into their morphology, allowing their fronds to be as flexible as those of uncalcified seaweeds. To provide the flexibility required by this structural innovation, the joint material of Calliarthron cheilosporioides, a representative articulated coralline alga, relies on an extraordinary tissue that is stronger, more extensible and more fatigue resistant than the tissue of other algal fronds. Here, we report on experiments that reveal the viscoelastic properties of this material. On the one hand, its compliance is independent of the rate of deformation across a wide range of deformation rates, a characteristic of elastic solids. This deformation rate independence allows joints to maintain their flexibility when loaded by the unpredictable - and often rapidly imposed - hydrodynamic force of breaking waves. On the other hand, the genicular material has viscous characteristics that similarly augment its function. The genicular material dissipates much of the energy absorbed as a joint is deformed during cyclic wave loading, which potentially reduces the chance of failure by fatigue, and the material accrues a limited amount of deformation through time. This limited creep increases the flexibility of the joints while preventing them from gradually stretching to the point of failure. These new findings provide the basis for understanding how the microscale architecture of genicular cell walls results in the adaptive mechanical properties of coralline algal joints.