Polyploidy is considered a driving force in plant evolution and domestication. Although in the genus Arachis, several diploid species were traditionally cultivated for their seeds, only the allotetraploid peanut Arachis hypogaea became the successful, widely spread legume crop. This suggests that polyploidy has given selective advantage for domestication of peanut. Here, we study induced allotetraploid (neopolyploid) lineages obtained from crosses between the peanut’s progenitor species, Arachis ipaënsis and Arachis duranensis, at earlier and later generations. We observed plant morphology, seed dimensions, and genome structure using cytogenetics (FISH and GISH) and SNP genotyping. The neopolyploid lineages show more variable fertility and seed morphology than their progenitors and cultivated peanut. They also showed sexual and somatic genome instability, evidenced by changes of number of detectable 45S rDNA sites, and extensive homoeologous recombination indicated by mosaic patterns of chromosomes and changes in dosage of SNP alleles derived from the diploid species. Genome instability was not randomly distributed across the genome: the more syntenic chromosomes, the higher homoeologous recombination. Instability levels are higher than observed on peanut lines, therefore it is likely that more unstable lines tend to perish. We conclude that early stages of the origin and domestication of the allotetraploid peanut involved two genetic bottlenecks: the first, common to most allotetraploids, is composed of the rare hybridization and polyploidization events, followed by sexual reproductive isolation from its wild diploid relatives. Here, we suggest a second bottleneck: the survival of the only very few lineages that had stronger mechanisms for limiting genomic instability.