This paper analyses the unsteady stagnation-point flow of Oldroyd-B-power-law nanofluid, which has the characteristics of viscoelasticity and shear thinning simultaneously. Modified Cattaneo–Christov heat flux modelis used to describe thermal relaxation and thermal retardation in the heat transfer process. Meanwhile, different from the viscous dissipation of Newtonian fluid, based on the constitutive relation of Oldroyd-B–power-law fluid, the effect of relaxation–retardation viscous dissipation is studied. Additionally, 2 g/l xanthan gum solution is considered as the base fluid and copper oxide (CuO), aluminium oxide (Al$_2$O$_3$) and silver (Ag) with 5% volume fraction areused as nanoparticles. Their thermal conductivities are calculated by experiments. Utilising similar transformations, partial differential equations are cast into ordinary differential equations.And non-linear analyses are done by takingadvantage of the double-parameter transformation expansion method with the base function (DPTEM-BF) method. The outcome illustrates that the velocity holds an opposite trend for Deborah numbers for relaxation and retardationtimes. Furthermore, among the three nanofluids, Ag–xanthan gum nanofluid has the strongest ability to increase heat transfer, which can provide a theoretical basis for industrial processing.