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We introduce and analyze an optoelectronic mixer (OEM) based on the kinetic inductive photoresponse in high-temperature superconducting (HTS) films. This device combines photodetection and optoelectronic mixing functions through a nonlinear change in the kinetic inductance of the HTS film when it is irradiated by an optically modulated microwave signal. A comprehensive theoretical analysis is presented using the two-temperature model to describe the nonbolometric (quantum) photoresponse and the kinetic inductance model for the electrical part. Upon the optical irradiation, the change in the electron temperature of the HTS film leads to a parametric change in the kinetic inductance of the photoexcited HTS bridge, which in the presence of a bias current produces a periodic voltage waveform. In order to obtain the temporal behavior and the frequency content of the output voltage in terms of the input local oscillator and modulation frequencies, the kinetic inductance model and Fourier series analysis have been used and their physical consequences have been discussed in detail. The merit characteristics of the kinetic inductive HTS-OEM, such as intrinsic and optical conversion gains and noise temperature, are evaluated and compared with other high-frequency mixers. This is followed by the numerical simulation of the proposed device.