Probabilistic material flow analysis and graph theory were combined to calculate predicted environmental concentrations (PECs) of engineered nanomaterials (ENMs) in Swiss rivers: 543 river sections were used to assess the geographical variability of nano-TiO(2), nano-ZnO and nano-Ag, and flow measurements over a 20-year period at 21 locations served to evaluate temporal variation. A conservative scenario assuming no ENM removal and an optimistic scenario covering complete ENM transformation/deposition were considered. ENM concentrations varied by a factor 5 due to uncertain ENM emissions (15%-85% quantiles of ENM emissions) and up to a factor of 10 due to temporal river flow variations (15%-85% quantiles of flow). The results indicate highly variable local PECs and a location- and time-dependent risk evaluation. Nano-TiO(2) median PECs ranged from 11 to 1'623 ng L(-1) (conservative scenario) and from 2 to 1'618 ng L(-1) (optimistic scenario). The equivalent values for nano-ZnO and nano-Ag were by factors of 14 and 240 smaller.