Divers from the Civil Protection Agency, which normally responds to earthquakes, floods and avalanches, and police were to start exploring the 30m-deep lake today.
They will use sonar and other high-tech equipment in the hope of finding the remains of the fabled third ship, believed to be about 75m long.
They are working on information from fishermen who say that in one part of the lake their nets often get snagged and they haul up Roman artefacts.
"We know from documents from the 15th century that one of the boats went down in an area different to where the other two were found," said Alberto Bertucci, the local mayor.
It is not known how the huge craft ended up at the bottom of the lake. It may have been that they simply deteriorated over time and became waterlogged, or that Emperor Claudius had them sunk in condemnation of the excesses of his predecessor's reign. They were essentially floating palaces, decorated with gold, marble and mosaic floors and boasting luxurious facilities such as heating and plumbing.
It was said they were equipped with sails of purple silk and had richly decorated prows.
The on-board entertainment may even have extended to orgies.
The two boats recovered in the 1930s were kept in a museum that was almost completely destroyed in May 1944 in fighting between the Allies and German forces. A few charred timbers and some bronze figures were all that survived.
Caligula reigned from 37AD to 41AD and is generally depicted by historians as a depraved megalomaniac.
