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The strength of the adjustment towards arbitrage equilibrium can be expected to be somehow proportional to the extent of market price deviations from equilibrium. In this article, threshold and smooth transition cointegration models are applied to quarterly wheat prices of three major world suppliers over the period 1973–99. Results based on arranged autoregressions of the error term of a static regression do not prove to be robust. Although non-linear models relying on a multivariate system approach yield partly contradictory results, the main evidence from the latter suggests a weakening, rather than an outright inaction, of the adjustment process in the inner regime.