The relative competitive advantage of 12 commercially available wheat varieties was examined against Lolium rigidum Gaud. at a number of sites from 1995 to 1997 in south-eastern Australia. Nearly all the variation in crop grain yield was attributable to the variety × environment effects (81%), with only 4% due to variety × weed × environment effects. Some varieties exhibited an environment-specific competitive advantage, for example Katunga, Dollarbird and Hartog, whereas others like Shrike, Rosella and Janz were relatively poorly competitive in some situations. The introduction of greater genetic variability into wheat is required to significantly increase competitiveness. Alternatively, manipulating crop agronomy, such as increasing crop seeding rate, may be a practical alternative. The grain yield of weed-free wheat was highly positively correlated with grain yield of the weedy plots, suggesting that local adaptation is important for strong competitiveness, and that wheat breeders in southern Australia may be inadvertently selecting for competitive advantage with weeds when selecting for other traits such as early vigour. The varieties which showed competitive yield advantage also suppressed L. rigidum. A combination of short-term agronomic manipulations and a longer-term breeding effort is needed for increasing wheat competitiveness, and the increasing importance of herbicide-resistant weeds may facilitate this process. [ABSTRACT FROM AUTHOR]