Animal hairs existing broadly in nature are found to be effectively responsive to stimuli of heat and water in sequence for shape deformation and recovery, namely, coupled shape memory function (CSMF). In the paper, the ability of thermo-water sensitive CSMF was first time investigated for animal hairs, the structural and molecular networks for net-points and switches were therefrom identified. Experimentally, animal hair manifested a high ability of shape fixation in thermal processing and good shape recovery by water stimulus. Characterizations of two stimuli (heating and hydration) were performed systematically on hair's deformation, recovery, viscoelasticity and chemical components (crystalline phase, key bonds inamorphous area). The variations of related chemical components in molecular networks were also explored. A hybrid structural network model was thereafter proposed to interpret the thermo-water sensitive CSMF of hair. This study of two-sequential-stimuli CSMF is original and inspired to explore more complex functions of other smart natural materials and expected to make much smarter synthetic polymers.