Allopolyploidy has played a prominent role in organismal evolution, particularly in angiosperms. Allohexaploidization is a critical step leading to the formation of common wheat as a new species, Triticum aestivum, as well as for bestowing its remarkable adaptability. A recent study documented that the initial stages of wheat allohexaploidization was associated with rampant genetic and epigenetic instabilities at genomic regions flanking a retrotransposon family named Veju. Although this finding is in line with the prevailing opinion of rapid genomic instability associated with nascent plant allopolyploidy, its relevance to speciation of T. aestivum remains unclear. Here, we show that genetic instability at genomic regions flanking the Veju, flanking a more abundant retroelement BARE-1, as well as at a large number of randomly sampled genomic loci, is all extremely rare or nonexistent in preselected individuals representing three sets of independently formed nascent allohexaploid wheat lines, which had a transgenerationally stable genomic constitution analogous to that of T. aestivum. In contrast, extensive and transgenerationally heritable repatterning of DNA methylation at all three kinds of genomic loci were reproducibly detected. Thus, our results suggest that rampant genetic instability associated with nascent allohexaploidization in wheat likely represents incidental and anomalous phenomena that are confined to by-product individuals inconsequential to the establishment of the newly formed plants toward speciation of T. aestivum; instead, extensive and heritable epigenetic remodeling coupled with preponderant genetic stability is generally associated with nascent wheat allohexaploidy, and therefore, more likely a contributory factor to the speciation event(s).