They are purple with orange beaks and feet.
They moved into Big Bird's nest because cuckoos don't build nests and that was the first nest they saw. They then decided that they would leave when their egg hatched, but when the egg hatched, the father changed his mind and decided to wait until the baby grew older. However, the mother and baby agreed to move to the park, which they eventually did.
They have sort of a religion based on the letter C, because it's the first letter in their species (cuckoo bird). In fact their national anthem is basically C is for Cookie (song) rewritten to be C is for Cuckoo.
They also teach their babies the alphabet before they are hatched by singing the alphabet to their eggs. They, like most members of the cuckoo family, do not build nests.
Cathy's father and Carlotta's husband. He seems to be the sort of "leader" of the family, making most of the introductions and decisions. He is also very devoted to Cathy, as shown when she was the reason for him wanting to stay.
Cathy's mother and Claude's wife. She seems to be a bit quieter than Claude.
Cathy is the hatchling daughter of Claude and Carlotta. She was not hatched yet when her parents moved to Big Bird's nest so Big Bird sat on her egg, singing the alphabet. When she hatched out, she sang the alphabet over and over and thought Big Bird was her dad. Big Bird thought she was cute but found her singing the alphabet over and over a bit tedious. When her parents came back, they taught her the cuckoo national anthem. She agreed, along with her mother, to move to the park. It was Big Bird who named her.