Croc's family is seen only in the final cutscene of Croc 2 after Croc had beaten Baron Dante. The island that they lived on (dubbed Crocodile Island by fans) was accessed by the Professor Gobbo's airplane. Croc's father wears a blue and white striped full body suit, carries a pipe, and has a mustache. His mother wears a pink and white striped body suit, wears a hat, and has eyelashes and lipstick. Croc's younger sibling basically is just a miniature version of Croc, minus the backpack. The gender is currently unknown. We learn little about these characters in the short amount of time they are introduced.
On Crocodile Island, Croc's parents have three blue eggs in a basket. At the end of the final cutscene, Baron Dante is shown stealing these eggs. The object of the bonus levels is, essentially, to retrieve the three eggs from their various hiding spots.