Cellular Nonlinear Networks (CellNNs) represent a promising computational paradigm, renowned for their massively parallel operation and energy-efficient, and real-time multi-dimensional signal processing capabilities. The recent incorporation of memristors into CellNN architectures has notably enhanced their functionality by introducing analog, non-volatile memory elements that enrich the networks’ dynamic behavior. In this paper, we present a rigorous dynamical analysis and a structured methodology for designing multitasking operation in Memristor Cellular Nonlinear Networks (M-CellNNs). A distinctive outcome of this enhancement is the possibility of multitasking, where different operations can be performed with the same set of design parameters, and the executed task is determined solely by the memristor’s state. In this paper, we develop a rigorous dynamical analysis together with a structured methodology that enable the systematic design and reliable implementation of multitasking Memristor Cellular Nonlinear Networks (M-CellNNs). Methodologically, we extend the second-order Dynamic Route Map (DRM₂) technique by integrating vector-field-based phase plane analysis, significantly improving the visualization and analytical characterization of realistic memristor dynamics within M-CellNN cells. Additionally, we propose a systematic analytical framework to precisely define the parameter spaces necessary for achieving targeted multitasking operations. Using a practical operational amplifier-based M-CellNN cell design well-suited for prototyping and functionality testing, we demonstrate our methodology through the reliable execution of multitasking operations, exemplified by the CORNER-EDGE task. Our enhanced analytical tools provide intuitive insights into complex system dynamics, facilitating accurate parameter selection and significantly advancing the practical feasibility and reliability of multitasking M-CellNN implementations.