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As semiconductor devices have shrunk further into the nanoscale regime, a new device, the memristor, has been discovered that has the potential to transform neuromorphic computing systems. This device is considered as the fourth fundamental circuit element. It was first theorized by Dr. Leon Chua in 1971 and has been discovered by HP labs in 2008. This paper describes initial efforts at fabricating the memristor devices and examining their properties. Two versions of memristor devices have been fabricated at the University of Dayton and the Air Force Research Laboratory utilizing varying thicknesses of the TiO2 dielectric layers. Our results show that the devices do exhibit the characteristic hysteresis loop in their I-V plots. Further refinement in the devices to achieve stronger hysteresis will be carried out as future work.