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This paper studies the theory of traveling-wave photodetection in superconductive multilayer optical waveguides, as a general platform for ultrafast, ultrasensitive, and ultralow-noise optoelectronics. The kinetic inductance theory of superconductive thin films and the modified transmission line theory are employed to investigate the distributed photodetection and signal generation mechanisms in superconductive traveling-wave devices. A general model for calculation of the optical responsivity of superconductive traveling-wave photodetectors is developed and operation regimes of interest are highlighted. Moreover, the inclusion of a photoconductive layer in the device structure and some important loading schemes are discussed and their effects on the device performance, such as quantum efficiency and electrical bandwidth, are addressed.