World | Agence-France Presse | Updated: February 28, 2014
The pair born in January belong to a rare species of African penguins, the only ones still found on the continent.
The workers at the zoo in Szegad - about 170 kilometres(105 miles) from Budapest - have set up areas for the penguin family and both parents are taking part in bringing up the little ones.
Lila and Gelb are between 40 to 60 centimetres (16 to 24 inches) long and weigh between two to four kilos (2.2 to 8.8 pounds).
The penguins belong to a species with a population of less than 200,000 - a tenth of what it was a century ago - and it is not unusual for them to be born in captivity.
Life expectancy is greater at the zoo, about 20 years compared with 10 years in the wild.
The Szeged zoo founded in 1989 is the newest and the largest one in Hungary comprising an area of 45 hectares (110 acres).