Cross-spectrum analysis based on linear correlations in the time domain suggested a coupling between large river flows and the El Ni¿o-Southern Oscillation (ENSO) cycle. A nonlinear measure based on mutual information (MI) reveals extrabasinal connections between ENSO and river flows in the tropics and subtropics, that are 20--70% higher than those suggested so far by linear correlations. The enhanced dependence observed for the Nile, Amazon, Congo, Paran¿, and Ganges rivers, which affect large, densely populated regions of the world, has significant impacts on inter-annual river flow predictabilities and, hence, on water resources and agricultural planning.