In this study, the bipolar resistive switching behavior of Pulsed Laser Deposited Zn1-xMgxO (x= 0, 0.1) thin films in Ag/Zn1-XMgxO/Cu structure has been investigated. The XRD pattern of Zn1-XMgxO exhibits the presence of (002) and (103) reflection. The cross-sectional field emission scanning electron microscopy (FE-SEM) studies were further carried out to examine the thickness of the film. In order to analyze the bipolar resistive switching behavior of the Zn1-xMgxO thin films, an I-V measurement was performed at room temperature. The memory cell Ag/Zn0.9Mg0.1O/Cu exhibits set voltage (ON state) at 2.57V and reset voltage (OFF state) at -3.15 V, excellent OFF to ON resistance ratio (~10 5 ) for 200 DC sweep cycles and exhibits good retention (>10 3 s). The physical mechanism responsible for exhibiting switching behavior in the Zn1-xMgxO thin films was explained by formation and rupture of the nano-scale conduction filament due to Oxygen vacancies. Ohmic conduction and Poole-Frenkel emission are responsible for current conduction in Low Resistance State (LRS) and High Resistance State (HRS) regions respectively. Enhanced switching behavior is observed by substitution of Mg in ZnO thin film. Nonvolatile two resistance states of the Zn1-XMgxO thin film could prove useful in future power efficient memory devices.