‘Big Top’ nectarine [Prunus persica (L.) Batsch] has appreciable keeping quality because it resembles, at ripening, the stony hard (SH) peach (P. persica) in firmness and crispness but melts at a slow speed at full ripening. We have characterized the postharvest behavior of ‘Big Top’ fruit, treated or not with ethylene for 5 days after harvest (DAH), and compared it with that of a SH peach (‘Ghiaccio’). Pp-ACS1 expression, ethylene evolution, endo-polygalacturonase (endo-PG) production, and softening were evaluated and compared with those of the physiologically ripe melting flesh (M) cultivar Bolero. Like ‘Bolero’, ‘Big Top’ fruit expressed Pp-ACS1 and evolved ethylene but with a 5-day delay. Pp-endo-PG expression, production of an active endo-PG, and fruit melting showed a parallel behavior; ethylene treatment enhanced all these features. In SH ‘Ghiaccio’ Pp-ACS1 expression, ethylene evolution, endo-PG production, and softening were absent during the first 5 DAH in air. ‘Ghiaccio’ neither expressed Pp-ACS1 nor evolved ethylene even after ethylene treatment but responded by accumulating Pp-endo-PG transcripts and an active endo-PG protein, with flesh melting. A ‘Big Top’ Pp-endo-PG clone showed several single nucleotide (SNP) and insertion-deletion (InDel) polymorphisms in comparison with the M Pp-endo-PG clone of ‘Bolero’ and substantial similarity with the Pp-endo-PG clone of ‘Ghiaccio’. In ‘Big Top’, we identified a peculiar SNP (bp 348) and InDels shared with ‘Ghiaccio’, possibly suitable for discriminating among different genotypes. Overall, the data confirm the pivotal role of ethylene in the regulation of endo-PG production and in the determination of peach flesh texture and support the evidence that ‘Big Top’ could be classified as a melting (slow-melting) phenotype.