Armed with large bottles of milk, William and Kate fed the hungry animals who were impatient to get their meal and bellowed when they first saw rangers approaching with the flasks.
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The Duke and Duchess were visiting Kaziranga National Park, home to elephants, water buffalo, the endangered swamp deer, tigers and two-thirds of the world's population of Indian one-horned rhinoceroses.
The park in the state of Assam in the north east of India is a unique mix of grasslands, wetlands and forest. It measures more than 800,000 square kilometres and is designated a Unesco World Heritage Site.
Earlier the Cambridges had a two-hour jeep safari into the heart of Kaziranga and gave a rhino a wide birth when they found it blocking their path.
They joked with village elders during a visit to a community in the park that two-year-old Prince George was "too naughty" to bring to India and would be running around.
Kate also said that seeing the local children, especially the young girl dancers, had reminded her how much she missed her own daughter Princess Charlotte, who is one next month.
William, who is a passionate conservationist, and Kate were introduced to the young animals at the Centre for Wildlife Rehabilitation and Conservation (CWRC).
It provides emergency care and rehabilitation for wild animals that have been injured, displaced or orphaned.
In a large area of grassland and sparse woodland the baby animals had gathered under the shade of a tree waiting for the royal couple who walked towards them.
The parental instincts of the Cambridges - who decided not to bring their two children on their seven-day tour of India and Bhutan - came to the fore during the encounter.
William and Kate fed all the animals in turn, crouching over the tiniest of the group - two female elephants and a rhino - to make sure they got every drop of milk, and also turning their attention to the older ones.
They were fed a milk formula every few hours with added coconut oil as a supplement.
Among the youngest was elephant Murphuli, who was just four weeks old when she was found in a tea garden trench in October last year.
The centre's vets hoped a female who rushed forward and examined the infant with her trunk was the mother but she was found in the same spot the next day.
Buree was another orphan elephant found, aged two months, a few days after Murphuli when she was rescued by villagers from a rocky pit, and after recovering from a swollen hip she is making friends with the other animals.
But it was Dunga the rhino, the smallest and newest resident at the centre, who won Kate's heart. The youngster was found alone by forest staff on patrol and when they failed to locate the mother he was taken to the centre.
As the couple fed the elephants some stretched out their trunks towards the bottles and all tipped their heads back to get every drop.
William and Kate gave the animals comforting rubs as they fed them, scratching the tops of their heads and patting their trunks.
Vivek Menon, chief executive officer of the Wildlife Trust of India which established the CWRC with a number other bodies, joined the royal couple for the encounter with the animals.
He said: "They were absolutely thrilled and loved being with the animals. The Duchess loved the baby rhino particularly.
"The Duke said if he could he would have spent the whole day there."