This study reports intrinsic multimodal memristivity of a nonconjugated radical polymer with ambient stability. Organic memristive devices represent powerful candidates for biorealistic data storage and processing. However, there exists a substantial knowledge gap in realizing the synthetic biorealistic systems capable of effectively emulating the cooperative and multimodal activation processes in biological systems. In addition, conventional organic memristive materials are centered on conjugated small and macromolecules, making them synthetically challenging or difficult to process. In this work, we first describe the intrinsic resistive switching of the radical polymer that resulted in an exceptional state retention of >105 s and on/off ratio of >106. Next, we demonstrate its bimodal cooperative switching, in response to the proton accumulation as a biological input. Last, we expand our system toward an advanced in-sensor computing system. Our research demonstrates a nonconjugated radical polymer with intrinsic memristivity, which is directly applicable to future electronics including data storage, neuromorphics, and in-sensor computing.