These babies are appearing in a new BBC programme called Orangutan Diary.
In the show, presenters Michaela Strachan and Steve Leonard, follow the stories of these endangered creatures.
Lots of the orangutans living at the centre in Borneo, south-east Asia, were orphans when they arrived. They centre looks after them until they're big and strong enough to return to the wild.
This little monkey is chewing on a piece of fruit!
And this one is checking out the camera equipment and looking through the view finder!
Experts say orangutans are endangered because the jungle they live in is being chopped down to plant other things. It's thought they could be nearly extinct by 2012 unless something isn't done to save them.