As a result of enormous progress in nanoscale electronics, interest in Artificial Intelligence (AI) supported systems has also increased greatly. These systems are typically designed to process computationally intensive data. Parallel processing neural network architectures are particularly noteworthy for their ability to process dense data at high speeds, making them suitable candidates for AI algorithms. Due to their ability to combine processing and memory functions in a single device, memristors offer a significant advantage over other electronic platforms in terms of area scaling efficiency and energy savings. In this study, single-layer and bilayer metal-oxide HfOx and TiOy memristor devices inspired by biological synapses were fabricated by pulsed laser and magnetron sputtering deposition techniques in high vacuum with different oxide thicknesses. The structural and electrical properties of the fabricated devices were analysed using X-ray reflectivity (XRR), X-ray photoelectron spectroscopy (XPS), and standard two-probe electrical characterization measurements. The stoichiometry and degree of oxidation of the elements in the oxide material for each thin film were determined. Moreover, the switching characteristics of the metal oxide upper layer in bilayer devices indicated its potential as a selective layer for synapse. The devices successfully maintained the previous conductivity values, and the conductivity increased after each pulse and reached its maximum value. Furthermore, the study successfully observed synaptic behaviours with long-term potentiation (LTP), long-time depression (LTD), paired-pulse facilitation (PPF), and spike-timing-dependent plasticity (STDP), showcasing potential of the devices for neuromorphic computing applications.