Linear and nonlinear (in both steady and transient shear flows) rheological properties of polymer/layered silicate nanocomposites prepared by melt mixing of poly(butylene succinate-co-adipate) and organically modified montmorillonite are investigated. Morphology of the nanocomposites is observed by x-ray diffraction and by transmission electron microscopy. Linear viscoelastic measurements in oscillatory shear with small strain amplitude show a low frequency plateau for storage modulus (an indication of a pseudo-solid like structure). A strong shear-thinning behavior for all ranges of shear rates is observed for high clay loading. An unusual behavior is observed for steady state normal stress differences. At low shear rates their values are larger than those observed for pure polymer. An inverse relation is observed at relatively high shear rates. The two models [Eslami, H., M. Grmela, and M. Bousmina, "A mesoscopic rheological model of polymer/layered silicate nanocomposites," J. Rheol. 51, 1189-1222 (2007); Eslami, H., M. Grmela, and M. Bousmina, "A mesoscopic tube model of polymer/layered silicate nanocomposites," Rheol. Acta 48, 317-331 (2009)] that we have developed previously allow us to relate the observed rheological behavior to the physics taking place in the nanocomposites on a mesoscopic level. The models take into account the chain-chain, chain-lamella, and lamella-lamella interactions. With their help, we are also able to separate contributions from the polymer and the nano charge. (C) 2010 The Society of Rheology. [DOI: 10.1122/1.3372720]