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Amaranthus retroflexus L. and Chenopodium album L. (Amaranthaceae) are weedy plants that cause severe ecological and economic damage. In this study, we collected DNA from three different countries and assessed genetic diversity using inter-simple sequence repeat (ISSR) markers. Our analysis shows both weed species have low genetic diversity within a population and high genetic diversity among populations, as well as a low value of gene flow among the populations. UPGMA clustering and principal coordinate analysis indicate four distinct groups for A. retroflexus L. and C. album L. exist. We detected significant isolation-by-distance for A. retroflexus L. and no significant correlation for C.album L. These conclusions are based data from 13 ISSR primers where the average percentage of polymorphism produced was 98.46% for A. retroflexus L. and 74.81% for C. album L.These data suggest that each population was independently introduced to the location from which it was sampled and these noxious weeds come armed with considerable genetic variability giving them the opportunity to manifest myriad traits that could be used to avoid management practices. Our results, albeit not definitive about this issue, do not support the native status of C. album L. in Iran.