Abstract: The memory effect plays a critical role in accurately characterizing the nonlinear accelerated creep stage of rock deformation. Using hydrous mudstone as the research object, triaxial compression tests, creep tests, and microstructural analyses were conducted on mudstone specimens with varying water contents. The results reveal the softening behavior of the elastic modulus with increasing water content and determine the long-term creep strength of water-bearing mudstone, demonstrating the significant influence of water on the deterioration of mudstone microstructure. Based on these findings, macroscopic and mesoscopic damage variables were defined using elastic modulus softening and pore fractal dimension, respectively, and a Burgers creep damage constitutive model was developed. Furthermore, based on the theory of memory-dependent derivatives, a modified memory-dependent derivative was proposed, and a stress-switch-controlled dashpot element capable of describing nonlinear accelerated creep behavior was established. This element features a memory effect that does not decay over time and possesses clear physical significance. Finally, the dashpot element was connected in series with the Burgers creep damage model to construct a creep damage constitutive model that accounts for permanent memory effects. This model comprehensively incorporates the initial macroscopic and mesoscopic damage characteristics of mudstone under different water contents. The accuracy and superiority of the proposed model were validated through triaxial creep test results on mudstone with varying water contents and comparative calculations with other creep models. These findings provide a theoretical foundation for analyzing the long-term stability of geotechnical engineering structures.