Present work has been studied the stagnation-point flow of hybrid Ag-CuO/water nanofluids over the stretching/shrinking sheet. The Navier-Stokes equations have reduced to the ordinary differential equations with similarity transformation. Runge-Kutta Fehlberg (RKF45), together with the shooting method, is employed to solve the differential equations. Numerical analysis showed that dual solutions exist and are connected to the specific values of the shrinking rate. All figures have the same behavior with the suction/injection parameter. Furthermore, with the intensification of the suction/injection parameter, the graphs are contracted, and the lower solutions become extended. The friction factor of Ag/water and hybrid nanofluids is increased by about 50-70% and 35-50% with suction/injection parameter, respectively. Normalized Nusselt number for Agiwater and hybrid nanofluids arc increase by about 150-200% and 100% with suction/injection parameter, respectively. Time-dependent stability analysis showed that only the upper branch of solutions is stable, while the lower branch is not in actual physics. (C) 2020 Elsevier B.V. All rights reserved.