The unusual big cats were born to ligress Zita, a cross between an African lion and a Bengal tigress.
The latest arrivals - born in June at Novosibirsk Zoo - have not been named yet and will be offered to other zoos around the world. They were born to Zita and were fathered by Samson, an African lion.
The pair first produced a liligress, a female cub, in 2012, and a year later Zita gave birth to three cubs - all female.
Such offspring are known as 'hybrids', and Zita could not have been born in the wild.
Deputy zoo director Olga Shilo denied the zoo is deliberately seeking to breed hybrids. She also said the cubs are healthy.
'We did not try to breed them specifically,' she said. 'On the contrary we tried to split them always, but ... We're not striving to breed hybrids.'
She has said previously that there was genuine surprise when Zita was conceived and born.
'Zita's parents have known each other since their early days, when they were quite young,' she said.
'The keepers saw that they overcame any natural enmity but we had no idea they would, or even could, mate.
'Everyone was more than a little surprised when a flame of passion consumed these two very different childhood friends.'
Archeologists discovered a new stone bracelet, two sharp pins, a marble ring and fox tooth pendants.