The male cubs were born on Thursday, June 16 to mother Maliya and father Lucifer.
Until now Maliya has been tucked away caring for the cubs with her own mother, Indu, who was born at Paignton Zoo and who is now a granny.
Asiatic lions are officially classed as Endangered; just 15 have been born in zoos around the world so far this year.
Neil Bemment, the zoo's curator of mammals, said: "They have come through their critical first few weeks and are now quite mobile. We have been really pleased with how Maliya has been getting on with being a new mum – she has done a good job so far.
"We hope visitors to Paignton Zoo will get to see the cubs soon, but they will need to be patient – they have access to the public enclosure but Maliya may choose to keep them indoors or take them to a more private part of the paddock initially.
"We do have video footage of the cubs playing on site.CCTV cameras donated by Crimehalt Fire & Security have captured footage of the youngsters."
Factfile: Lions on the edgeAsiatic lions (Panthera leo persica) are threatened by hunting and habitat destruction. Fewer than 400 survive in the wild in the Gir National Park and Lion Sanctuary in India.
There are conservation breeding programmes in zoos including a European Endangered species programme.
The Asiatic lion is smaller than the African and has a distinctive fold of skin on the belly. The male's mane is smaller and lighter in colour.
Both sexes defend their territory by roaring, urine marking and patrolling.
The cubs are born after a gestation of about 105 days.
Read more at http://www.plymouthherald.co.uk/cute-or-what-asiatic-lion-cubs-make-their-debut/story-29562514-detail/story.html#Q5kESsWyUxq1o2oz.99