The pressure dependence of viscosity of two nanocomposites with a polystyrene (PS) matrix that contains, respectively, multiwalled carbon nanotubes (MWCNTs) and graphene, was investigated. Two procedures were used: (a) Pressure-volume-temperature (PVT) results to obtain the pressure coefficient beta(0) for Newtonian viscosity and (b) measurements in a pressure chamber in a capillary rheometer, to obtain the pressure coefficient at constant shear rate, beta' and the pressure coefficient at constant shear stress, beta ''. PVT results revealed that the most significant differences between the samples concerned the variation of the glass transition with pressure, dTg/dP, which was concomitant with the number of polymer chains fixed on the surface of the nanofillers. Pressure chamber results showed that the pressure coefficient beta '' was similar for PS and the nanocomposites, at the shear rates involved in processing. For the first time, the piezorheological complexity of nanocomposites was analyzed, together with the thermorheological complexity. PS/MWCNT nanocomposite was thermorheologically complex in the linear viscoelastic regime, but thermorheologically and piezorheologically simple in the shear thinning flow region. Nevertheless, PS/graphene nanocomposite was thermorheologically and piezorheologically complex in the linear viscoelastic regime and the shear thinning regime. This was due to the high capacity of graphene 2D platelets to retain polymer chains anchored to its surface. (C) 2016 The Society of Rheology.