Ducks (common, Muscovy and mule ducks) are the third most important bird species in animal production for human consumption worldwide. Our study aimed to improve the efficiency of mule duck breeding, thus contributing to the efficiency of food production in general. In the common duck, females can be bred either with males of the same species (i.e. in pure breeding (PB) subscript p) or in inter-generic crossbreeding (CB; subscript c) with Muscovy drakes to produce the hybrid mule duck. The aim of the present study was to estimate the genetic parameters of several indicators of duration of fertility, considered to be a trait of the female duck, within and between breeding schemes and, in particular, to estimate the purebred–crossbred genetic correlation (rgpc). These indicators were maximum duration of fertility (MD), that is, the time interval between insemination and the last fertilised egg, the number of fertile eggs (F) and of hatched ducklings (H) after a single artificial insemination (AI), and the fertility rate over days 2 to 12 after AI (F2,12), taking three sub-periods (F2,4, F5,8, F9,12) into account. A total of 494 females and 2655 inseminations were involved. PB resulted in longer duration of fertility (MDp = 8.1 v.MDc = 6.4 days). Heritability (h2) was higher for MDp (estimate ± s.e.: 0.27 ± 0.04) than for MDc (0.15 ± 0.04), but both traits were highly correlated with each other (rgpc = 0.85 ± 0.07). Fp and Fc had similar heritability (h2 around 0.24) and displayed a high genetic correlation (0.78 ± 0.07). The same was true for Hp and Hc (h2 around 0.17 and rgpc = 0.88 ± 0.05). The heritability estimates were 0.24 ± 0.03 for F2,12p and 0.20 ± 0.04 for F2,12c, with a 0.80 ± 0.07 genetic correlation between each other. Permanent environmental effects influenced MDp far less than MDc, Fp less than Fc, but Hp and Hc to the same extent. The high values for rgpc (>0.78) indicated that the same genes are involved in the duration of fertility for both PB and CB. Unlike CB, initial fertility for PB (F2,4p) was not correlated to overall fertility rate and to duration of fertility and probably involves different genes, if any. In both breeding schemes, indirect selection on F would be better than direct selection on H to improve H, and easier to implement than selection on MD. Moreover, any gain in one breeding scheme will have its correlated counterpart in the other one, because of the high values of rgpc.