Non-linear adjustment towards long-run equilibrium in the sugar-ethanol-oil nexus in Brazil is examined. We develop generalised bivariate error correction models that allow for cointegration between variables, where dynamic adjustments are potentially non-linear functions of the disequilibrium errors. Linear error correction models and threshold models are specific cases within this generalised structure. The models are estimated using Bayesian Monte Carlo Markov Chain algorithms and applied to oil, sugar and ethanol prices. Bayesian model selection methods suggest that the long-run drivers of Brazilian sugar prices are oil prices and that there are nonlinearities in the adjustment processes of sugar and ethanol to oil, but linear adjustment between ethanol and sugar. Threshold adjustment is supported between ethanol and oil and asymmetric adjustment between sugar and oil. Bayesian model averaging is used to estimate the elasticities of transmission from oil to sugar and ethanol.