The reptiles, Paleo and Suchus, have been taught to listen for their names being called, it was claimed.
Keepers at the centre in Ellesmere Port, Merseyside, they are even learning when to open their mouths for food.
They ssaid the type of training had worked with mammals before but hardly ever with reptiles.
"They are very intelligent and started responding to their names in just a few days," said Tom Cornwall, the aquarium's manager.
In a bid to train them, the crocodiles, which are called Cuvier's dwarf caiman, are given food as a prize if they react in the right way.
The training takes its idea from a similar scheme run at the Madras Crocodile Bank Trust in India.
Once fully trained, the aquarium's zoological team will set up "enrichment activities" for the pair.
Mr Cornwall, Blue Planet Aquarium's ranger and exhibits manager, added: "As well as enabling us to approach them and inspect and treat any potential health issues it will also allow us to set up tasks and foraging exercises for them to mimic the types of behaviour they would have to use in the wild."
Found throughout South America, the Cuvier's dwarf caiman usually live in freshwater habitats like rivers, including the Amazon, flooded forests and larger lakes.