The thesis investigates the utilization of memristive and memcapacitive crossbar arrays in low-power machine learning accelerators, offering a comprehensive co-design framework for deep neural networks (DNN). The model, implemented through a hybrid Python and PyTorch approach, accounts for various non-idealities, achieving exceptional training accuracies of 90.02% and 91.03% for the CIFAR-10 dataset with memristive and memcapacitive crossbar arrays on an 8-layer VGG network. Additionally, the thesis introduces a novel approach to emulate meminductor devices using Operational Transconductance Amplifiers (OTA) and capacitors, showcasing adjustable behavior. Transistor-level simulations in 180 nm CMOS technology, operating at 60 MHz, demonstrate the proposed meminductor emulator's viability with a power consumption of 0.337 mW. The design is further validated in neuromorphic circuits and CNN accelerators, achieving training and testing accuracies of 91.04% and 88.82%, respectively. Notably, the exclusive use of MOS transistors ensures the feasibility of monolithic IC fabrication. This research significantly contributes to the exploration of advanced hardware solutions for efficient and high-performance machine-learning applications.