Priests Nicola Corradi, an 83-year-old Italian, and 59-year-old Argentine Horacio Corbacho, as well as former gardener Armando Gomez, 49, are accused of sexual abuse, corruption of children and mistreatment at a Catholic school for deaf children, for which they could face up to 50 years in jail.
The case relates to the abuse of around 20 children from the Provolo Institute in the western town of Mendoza, founded in 1995, which Corradi headed until his arrest in November 2016.
The closed-doors trial, expected to last two months, will hear testimony from 13 victims who suffered abuse between the ages of four and 17, relating to 43 offences.
Outside the court, a group of young people who used to attend the institute held up placards saying: "Support for the Provolo survivors."
In a trial last year, former altar boy Jorge Bordon admitted to abusing five victims and was sentenced to 10 years in prison.
The Provolo Institute in Mendoza, 1,000 kilometers (600 miles) to the west of Buenos Aires, was closed in 2016 after the first accusations emerged of abuse that was allegedly carried out since 2004.
Corradi came to Argentina in 1970 from the original Provolo Institute in Verona -- which has also been shaken by a pedophilia scandal in recent years -- to run the Provolo in La Plata, before transferring to the Mendoza institute in 1998.