This paper presents a nonlinear viscoelastic model for polymer nanocomposites and the computed model response to large amplitude oscillatory shear flow. The model predicts the stress in a mixture of entangled polymer chains, with different convective constraint release (CCR) rates for free chains and nanoparticle-attached chains, through an averaging scheme which is consistent with double reptation in the Marrucci-Ianniruberto constitutive equation. The nonlinear response of the mixture is evaluated both numerically in terms of Q and by an asymptotic analysis in terms of four frequency dependent parameters of medium amplitude oscillatory shear (MAOS) as well as the intrinsic nonlinearity parameter Q(0). In the case of free polymer chains alone, the MAOS signatures are comparable to those of the Giesekus model with the notable difference of a minimum in the elastic parameter [e(1)] at De >1. The viscous nonlinear parameters of the mixture model depart significantly from those of the free chains, especially in mixtures where the CCR parameter for attached chains is larger than that for the free chains: [v(1)] has a prominent minimum and [v(3)] has a prominent maximum near De = 2/c, the low frequency plateau region, along with a higher Q(0) compared to the matrix at all Deborah numbers. (c) 2018 Wiley Periodicals, Inc.