Homoploid hybrid speciation has been recognized for its potential rapid completion, an idea that has received support from experimental and modeling studies. Following initial hybridization, the genomes of parental species recombine and junctions between chromosomal blocks of different parental origin leave a record of recombination and the time period before homogenization of the derived genome. We use detailed genetic maps of three hybrid species of sunflowers and models to estimate the time required for the stabilization of the new hybrid genome. In contrast to previous estimates of 60 or fewer generations, we find that the genomes of three hybrid sunflower species were not stabilized for hundreds of generations. These results are reconciled with previous research by recognizing that the stabilization of a hybrid species' genome is not synonymous with hybrid speciation. Segregating factors that contribute to initial ecological or intrinsic genetic isolation may become stabilized quickly. The remainder of the genome likely becomes stabilized over a longer time interval, with recombination and drift dictating the contributions of the parental genomes. Our modeling of genome stabilization provides an upper bound for the time interval for reproductive isolation to be established and confirms the rapid nature of homoploid hybrid speciation.