Activation of transposable elements in species' genomes represents an important mechanism of new mutation and of potential rapid change in genome size. Thus, it is increasingly recognized that transposable elements likely have played a significant role in shaping species' evolution. In an earlier report, we showed that the genomes of three sunflower species of ancient hybrid origin have experienced large-scale proliferation events of sequences within the Ty3/gypsy-like superfamily of long terminal repeat (LTR) retrotransposons. In this report, we investigate whether another superfamily of LTR retrotransposon (Ty1/copia-like elements) have experienced similar derepression and proliferation events in the genomes of these sunflower hybrid taxa. We show that Ty1/copia-like elements also have undergone copy number increases following or associated with the origins of these species, although the scale of proliferation is less than that for Ty3/gypsy-like elements. Surveys of sequence heterogeneity of Ty1/copia-like elements in the genomes of the three hybrid and two parental species' genomes reveal that a single sub-lineage of these elements exhibits characteristics of recent amplification, and likely served as the proliferative source lineage. These findings indicate that the genomic and/or environmental conditions associated with the origins of these sunflower hybrid taxa were conducive to derepression of at least two major groups of transposable elements.