Summary The hygienic behaviour of the honey bees is considered to be a potential characteristic associated with resistance to Varroa destructor n.sp. In this study the heritability of the hygienic behaviour of Apis mellifera L. bees was estimated on the basis of the mother–daughter regression. Data were obtained from measurements of the bees' hygienic behaviour towards V. destructor-infested cells and towards pin-killed sealed brood. The heritability for the hygienic behaviour towards V. destructor-infested brood cells was h2 = 0.18 (± 0.27) and h2 = 0.36 (± 0.30) for the hygienic behaviour towards dead brood cells. The repeatability was likewise higher for the pin-killed brood assay (W = 0.46) compared with the assay using living mites-infested brood cells (W = 0.24). The genetic correlation between the behavioural responses to either the mite-infested or pin-killed brood cells was calculated to be rg = 0.61 (± 0.51) and the phenotypic correlation to be rp = 0.11 (p = 0.28, n = 100). Since hygienic colonies demonstrate resistance to brood diseases such as American foulbrood and chalkbrood, it may be worthwhile to intensify the expression of the hygienic behaviour through selective breeding and thus strengthen these potential characteristics associated with resistance to V. destructor in honey bee stock.