Studies were conducted to determine the critical period of smooth amaranth interference in watermelon (Citrullus lunatus L.) and muskmelon (Cucumis melo L. var. reticulatus). Best-fit linear or exponential regression models were used to predict the maximum period of competition and the minimum weed-free period for 10% yield loss. The maximum period of competition and minimum weed-free period was 0.50 and 2.97 weeks after watermelon emergence, respectively, and 1.0 and 3.9 weeks after muskmelon emergence, respectively. The critical periods of smooth amaranth interference for the crops were between those intervals. In both crops, late emerging smooth amaranth had little effect on total yield. Smooth amaranth introduced at crop emergence reduced total yield. The effect of competition on yield components, i.e., fruit number per hectare and fruit mass, varied by crop. Muskmelon fruit count was more sensitive to smooth amaranth competition than was watermelon fruit count. Conversely, mass per fruit of muskmelon was less sensitive to this competition than was mass per fruit of watermelon.