Turnipweed [Rapistrum rugosum (L.) All.] and Mexican pricklepoppy (Argemone mexicana L.) are increasingly prevalent in the northern cropping regions of Australia. The effect of different densities of these two weeds was examined for their potential to cause yield loss in wheat (Triticum aestivum L.) through field studies in 2016 and 2017. There was 72% to 78% yield reduction in wheat due to competition from R. rugosum. Based on the exponential decay model, 18.2 and 24.3 plants m^–2 caused a yield reduction of 50% in 2016 and 2017, respectively. Rapistrum rugosum produced a maximum of 32,042 and 29,761 seeds m^–2 in 2016 and 2017, respectively. There was 100% weed seed retention at crop harvest. Competition from A. mexicana resulted in a yield loss of 17% and 22% in 2016 and 2017, respectively; however, plants failed to set seeds due to intense competition from wheat. Among the yield components, panicles per square meter and grains per panicle were affected by weed competition. The studies indicate a superior competitiveness of R. rugosum in wheat and a suppressive effect of wheat on A. mexicana. The results indicate that a wheat crop can be included in crop rotation programs where crop fields are infested with A. mexicana. High seed retention in R. rugosum indicates the possibility to manage this weed through seed catching and harvest weed seed destruction.