Long hydrological records, from the Amazon Basin, northeastern Brazil, and northwestern Peru spanning most of this century, are examined for trends in rainfall (three wettest months) and runoff (three months of highest flow) or stage, where no rating curves exist. Trends are tested for significance using the Mann-Kendall statistic. In basins where large soil, aquifer, or man-made reservoirs give rise to appreciable over-year storage, flows and water levels may be serially correlated. Where serial correlation exists, the usual statistical tests (linear regression, t-test, and Mann-Kendall) will overestimate the significance of trends, showing significance where none exists. Analysis for trend therefore requires particular care when data are serially correlated, and to avoid misleading results, additional supportive evidence must be sought. For example, rainfall records within the same river basin can be checked for trends; serial correlation in rainfall records, in particular, is less likely to be present, so the validity of any trends in rainfall is less open to question. Strong negative trends were found in flow data from the coast of northern Peru and the S¿o Francisco River, while positive significant trends were detected in the Parna¿ba River basin. No significant trends were found in the discharge or stage records from Amazonia, while rainfall in northeastern Brazil shows a slow increase over long periods. In the Parna¿ba and in some rivers of northern Peru unusually large discharges at the beginning or end of the records seem to account for the direction and significance of trends. ¿ 1998 American Geophysical Union