This work presents the results of the fabrication and investigation of flexible memristive structures based on parylene layers, which demonstrate stable resistive switching and are resistant to bends up to 10 mm radii. It is also proposed a two-step scheme for establishing the resistive state of the memristive structure, based on control of the value of the limiting current flowing through the structure. Obtained results open the possibility of using memristive structures based on parylene layers for neuromorphic computing systems and biocompatible "wearable" electronics.