The samples of Ga-doped Cr 2 O 3 system in rhombohedral crystal structure with space group R3 C were prepared by chemical co-precipitation route and annealing at 800 0 C.The current-voltage (I-V) curves exhibited many unique non-linear properties, e.g., hysteresis loop, resistive switching, and negative differential resistance (NDR). In this work, we report non-equilibrium properties of resistive switching and NDR phenomena. The non-equilibrium I-V characteristics were confirmed by repetiting measurement and time relaxation of current.The charge conduction process was understood by analysing the I-V curves using electrodelimited and bulk-limited charge conduction mechanisms, which were proposed for metal electrode/metal oxide/metal electrode structure. The I-V curves in the NDR regime and at higher bias voltage in our samples do not obeyed Fowler-Nordheim equation, which was proposed for charge tunneling mechanism in many thin film junctions. The non-equilibrium I-V phenomena were explained by considering the competitions between the injection of charge carriers from metal electrode to metal oxide, the charge flow through bulk material mediated by trapping/de-trapping and recombination of charge carriers at the defect sites of ions, the space charge effects at the junctions of electrodes and metal oxides, and finally, the out flow of electrons from metal oxide to metal electrode. electronic states. electric fields with alternate polarity, i.e., ON state (LRS) at one voltage polarity and OFF state (HRS) on reversing the voltage polarity. In abnormal bipolar resistive switching, the resistance state of the device is switched from LRS to HRS during positive polarity of electric field, and LRS to HRS during negative polarity of electric field. The abnormal resistive switching phenomenon has been observed in devices like Pt/GaO 3 /Pt [8] and Pt/TiO 2 /Pt [18]. Recently, thin films of BaTiO 3 [19] and ZnO [20] have shown the coexistence of resistive switching and negative differential resistance (NDR) behaviour ( < 0). The materials with room temperature NDR and resistive swirching are of increasing interest for applications in analog and digital circuits, including logic gates, voltage-controlled oscillator, and flip-flop circuit [21]. The additional feature of I-V loop is also important for applications of the materials in switching, low power memory, dynamic random access memory, static random access memory, and high storage density with long retention [22]. We present resistance switching and NDR phenomena at room temperature in a new material, developed by incorporating non-magnetic Ga atoms in the antiferromagnetic α-Cr 2 O 3 . The magnetic measurement [23] has shown Ga doped α-Cr 2 O 3 system as a diluted antiferromagnet with ordering temperature at about 50 K and a typical paramagnet at room temperature. This work is devoted to study the non-equilibrium I-V properties in thin pellet shaped samples of polycrystalline Ga doped α-Cr 2 O 3 system using Pt/CrGaO/Pt structure.The present transition metal oxide sample...