Obstructive sleep apnoea (OSA) is one of the major sources of the excessive daily sleepiness, cognitive dysfunction, and it increases cardiovascular morbidity and mortality. Previous studies suggested a possible genetic influence, based on questionnaires but no objective genetic study was conducted to understand the exact variance underpinned by genetic factors. Seventy-one Hungarian twin pairs involved from the Hungarian Twin Registry (48 monozygotic, MZ and 23 dizygotic, DZ pairs, mean age 51 ± 15 years) underwent overnight polysomnography (Somnoscreen Plus Tele PSG, Somnomedics GMBH, Germany). Apnoea hypopnea index (AHI), respiratory disturbance index (RDI) and oxygen desaturation index (ODI) were registered. Daytime sleepiness was measured with the Epworth Sleepiness Scale (ESS). Bivariate heritability analysis was applied. The prevalence of OSA was 41% in our study population. The heritability of the AHI, ODI and RDI ranged between 69% and 83%, while the OSA, defined by an AHI ≥5/h, was itself 73% heritable. The unshared environmental component explained the rest of the variance between 17% and 31%. Daytime sleepiness was mostly determined by the environment, and the variance was influenced in 34% by the additive genetic factors. These associations were present after additional adjustment for body mass index. OSA and the indices of OSA severity are heritable, while daytime sleepiness is mostly influenced by environmental factors. Further studies should elucidate whether close relatives of patients with OSA may benefit from early family risk based screening.