Via computer simulations, we investigate the linear and nonlinear viscoelastic response of polymer grafted nanoparticle networks subject to oscillatory shear at different amplitudes and frequencies. The individual nanoparticles are composed of a rigid spherical core and a corona of grafted polymers that encompass reactive end groups. With the overlap of the coronas on adjacent particles, the reactive end groups form permanent or labile bonds, and thus form a 'dual cross-linked' network. The existing labile bonds between particles can break and reform depending on the bond rupture rate, extent of deformation and the frequency of oscillation. We study how the viscoelastic behavior of the material depends on the energy of the labile bonds and identify the network characteristics that give rise to the observed viscoelastic response. We observe that with an increase in labile bond energy, the storage modulus increases while the loss modulus shows a more complex response depending on the labile bond energy. Specifically, in the case of the samples with the weaker labile bonds, the loss modulus increases monotonically, while for the samples with the stronger labile bonds, the loss modulus exhibits a minimum with an increase in frequency. We show that an increase in the storage modulus corresponds to an enhancement in the average number of bonds in the samples and the characteristics of the loss modulus depend on both the bond kinetics and the mobility of the particles in the network. Furthermore, we determine that the effective contribution of the bonds to the storage modulus decreases with increase in strain amplitude. In particular, while bond formation at small amplitude drives an increase in storage modulus, at large amplitudes it promotes clustering and formation of voids leading to strain softening. Our simulations provide a mesoscopic picture of how the nature of labile bonds affects the performance of cross-linked polymer-grafted nanoparticle networks. © 2014 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.