African swine fever (ASF) is a lethal hemorrhagic disease in domestic pigs and wild suids caused by African swine fever virus (ASFV), which threatens the swine industry globally. In its native African enzootic foci, ASFV is naturally circulating between soft ticks of the genus Ornithodoros, especially in the O. moubata group, and wild reservoir suids, such as warthogs (Phacochoerus spp.) that are bitten by infected soft ticks inhabiting their burrows. While the ability of some Afrotropical soft ticks to transmit and maintain ASFV is well established, the vector status of Palearctic soft tick species for ASFV strains currently circulating in Eurasia remains largely unknown. For example, the Iberian soft tick O. erraticus is a known vector and reservoir of ASFV, but its ability to transmit different ASFV strains has not been assessed since ASF re-emerged in Europe in 2007. Little is known about vector competence for ASFV in other species, such as O. verrucosus, which occurs in southern parts of Eastern Europe, including Ukraine and parts of Russia, and in the Caucasus. Therefore, we conducted transmission trials with two Palearctic soft tick species, O. erraticus and O. verrucosus, and the Afrotropical species O. moubata. We tested the ability of ticks to transmit virulent ASFV strains, including one of direct African origin (Liv13/33), and three from Eurasia that had been involved in previous (OurT88/1), and the current epizooties (Georgia2007/1 and Ukr12/Zapo). Our experimental results showed that O. moubata was able to transmit the African and Eurasian ASFV strains, whereas O. erraticus and O. verrucosus failed to transmit the Eurasian ASFV strains. However, naïve pigs showed clinical signs of ASF when inoculated with homogenates of crushed O. erraticus and O. verrucosus ticks that fed on viraemic pigs, which proved the infectiousness of ASFV contained in the ticks. These results documented that O. erraticus and O. verrucosus are unlikely to be capable vectors of ASFV strains currently circulating in Eurasia. Additionally, the persistence of infection in soft ticks for several months reaffirms that the infectious status of a given tick species is only part of the data required to assess its vector competence for ASFV.