We conduct tests for the presence of low-dimensional chaotic structure in the futures prices of four important agricultural commodities. Though there is strong evidence of non-linear dependence, the evidence suggests that there is no long-lasting chaotic structure. The dimension estimates for the commodity futures series are generally much higher than would be for low dimension chaotic series. Our test results indicate that autoregressive conditional heteroskedasticity (ARCH)-type processes, with controls for seasonality and contract-maturity effects, explain much of the non-linearity in the data. We make a case that employing seasonally adjusted price series is important in obtaining robust results via some of the existing tests for chaotic structure. Finally, maximum likelihood methodologies, that are robust to the non-linear dynamics, lend strong support to the Samuelson hypothesis of maturity effects in futures price changes. © 2002 Elsevier Science B.V. All rights reserved.