Recent empirical studies have found significant evidence of departures from competition in the input side of the Australian bread, breakfast cereal and margarine end-product markets. For example, Griffith (2000) found that firms in some parts of the processing and marketing sector exerted market power when purchasing grains and oilseeds from farmers. As noted at the time, this result accorded well with the views of previous regulatory authorities (p.358). In the mid-1990s, the Prices Surveillence Authority (PSA 1994)determined that the markets for products contained in the Breakfast Cereals and Cooking Oils and Fats indexes were "not effectively competitive"(p.14). The PSA consequently maintained price surveillence on the major firms in this product group. The Griffith result is also consistent with the large number of legal judgements against firms in this sector over the past decade for price fixing or other types of non-competitive behaviour. For example, bread manufacturer George Weston was fined twice during 2000 for non-competitive conduct and the ACCC has also recently pursued and won cases against retailer Safeway in grains and oilseeds product lines. Griffith obtained his results using highly aggregated data and a relatively simple empirical model. In this study we focus on confirming the earlier results by formally testing for competitive behaviour in the Australian grains and oilseeds industries using a more sophisticated empirical model and a less aggregated grains and oilseeds data set. We specify a general duality model of profit maximisation that allows for imperfect competition in both the input and output markets of the grains and oilseeds industries. The model also allows for variable-proportions technologies and can be regarded as a generalisation of several models appearing in the agricultural economics and industrial organisation literatures. Aggregate Australian data taken from the 1996-97 input-output tables are used to define the structure of the relevant industries, and time series data are used implement the model for thirteen grains and oilseeds products handled by seven groups of agents. The model is estimated in a Bayesian econometrics framework. Results are reported in terms of the characteristics of estimated probability distributions for demand and supply elasticities and indexes of market power. Our results suggest that there is a positive probability that: (a) flour and cereal food product manufacturers exert market power when purchasing wheat, barley, oats and triticale; (b) beer and malt manufacturers exert market power when purchasing wheat and barley; and (c) other food product manufacturers exert market power when purchasing wheat, barley, oats and triticale. What is interesting is that each of the transaction nodes where market power is indicated is one where a farm commodity is sold to a processing sector - that is, the evidence suggests oligopsonistic behaviour by grains buyers. The wheat and barley industries seem to be especially disadvantaged by this type of market conduct. A related and equally interesting result is that there was no consistent evidence of market power in the downstream nodes of the data set relating to the sales of flour and other cereal foods, or the sale of bread and other bakery products. These transaction points are where legal judgements against suppliers have been made in the recent past. We have stated our results in quite cautious language, as there is much uncertainty surrounding our estimates. This stems partly from the lack of good quality data, so we suggest that one avenue for future research should be improving the collection and integrity of relevant data (especially including the retail and distributive nodes of the various markets).