To integrate bipolar resistive switching cells into crosspoint structures, we serially connect a threshold-switching (TS) $\hbox{Pt}/\hbox{NbO}_{2}/\hbox{Pt}$ device with a memory-switching (MS) $\hbox{Pt}/\hbox{Nb}_{2}\hbox{O}_{5}/ \hbox{Pt}$ device and observe the suppression of the undesired sneak current. A simpler $\hbox{Pt}/\hbox{Nb}_{2}\hbox{O}_{5}/\hbox{NbO}_{2}/\hbox{Pt}$ bilayer oxide device was designed; it simultaneously exhibits TS and MS. The unique device characteristics in the metal/oxide/metal structure can be directly integrated into a crosspoint memory array without the diode; this can significantly reduce the fabrication complexity.