Gradual switching in the memristor or memcapacitor devices is the key parameter for the next generation of bio-inspired neuromorphic computing. Here, we have fabricated the WOx/ZrOx dual-oxide layered device, which shows the coexistence of gradual resistive and capacitive switching arisen from the current and capacitance hysteresis curves, respectively. The expansion of hysteresis loop can be modulated by altering the oxygen content in the oxide materials. Interestingly, the presence of negative differential resistance (NDR) is dependent on the voltage sweep direction and range of applied bias, which can be reasoned by the local electric field, charge trapping/detrapping, and conduction band offset at the dual-oxide interface. This study provides the concept of the coexistence of current and capacitance hysteresis along with NDR, and it is highly potential for memristor and memcapacitor circuits to explore neuromorphic computing.