Epoxy adhesives have been extensively used in the aerospace, marine, and automotive industries to join different components. A major concern with the use of epoxy adhesives is their viscoelastic behavior in aggressive service conditions such as hygrothermal ageing. Surveying the creep behavior of adhesives is of paramount importance to increase long-term durability. In this work, nanoindentation creep tests were performed on an epoxy adhesive exposed to distilled water and seawater at 55 °C for various ageing durations (0, 14, 38, 160, 251, 383, 582, and 800 h). The hardness, modulus, creep displacement, and creep rate sensitivity were quantitatively investigated to elucidate the effect of hygrothermal ageing. All the mechanical properties were found to decrease with the ageing time. The adhesive subjected to distilled water showed lower creep resistance due to higher absorption of moisture. In addition, linear relationships were observed between different mechanical properties and moisture contents irrespective of ageing conditions. Subsequently, the generalized Kelvin model was applied to investigate the creep compliance and the dependence of different deformation types (elastic, viscoelastic, and viscous deformation) on the ageing time and ageing conditions. The motion of molecular structures was also discussed. Finally, a modified creep model was proposed based on the generalized Kelvin model and continuum damage theories, which established the relationship between the dry and aged adhesive via the moisture-dependent degradation factors. The predicted creep displacements coincided well with the experimental results for the case, demonstrating the reliability of the creep model.