The accusations stem from the country's "Dirty War" from 1976 to 1983. During those years of military dictatorship, up to 30,000 students, labor leaders, intellectuals and leftists disappeared or were held in secret jails and torture centers.

(L to R) Reinaldo Begnone, Jorge Rafael Videla, Jose Luis Magnacco and Ruben Franco are accused of stealing babies.

Jorge Rafael Videla was among the coup leaders who overthrew then-President Isabel Martinez de Peron in March 1976. He ruled as dictator until 1981. Gen. Reynaldo Benito Bignone ruled the country from June 1982 until the nation's return to democracy in December 1983.

They are the two most high-profile defendants on trial for being the "presumed authors of the crimes of theft, retention and hiding of minors, as well as replacing their identities," according to a statement from the country's judiciary.

Specifically, the officers are being tried for the stealing of 34 babies from their parents, the court said.

Approximately 370 witnesses will be called to testify, according to the judiciary. The trial could take at least eight months to complete.

"The most real proof that there was a system in the thefts is the living proof, the children who regained their identities," said Agustin Chit, a lawyer for the Grandmothers of the Plaza de Mayo, who are among the plaintiffs. "It's all the documents that the grandmothers in these 33 years were able to collect. There is no perfect crime and there wasn't in this case in relation to the systematic plan. Even the bureaucracy of the state apparatus left behind many documents."

Neither the defendants nor their lawyers made comments as the trial got underway Monday, but in previous occasions have said that those incidents happened during a war and that the trial has a political angle and is not about finding the truth.

Carlos Pisani, whose parents were both kidnapped when he was only 37 days old, said that he's been waiting for more than three decades for justice to be done.

"We have fought for many years so that today we can have a country where we have justice," Pisani told CNN en Español.

Unlike others who were stolen and given a new identity, Pisani was raised by his grandmother, who told him from a young age about the circumstances surrounding his parents' disappearance. He has worked with a group of youths that include some of those whose cases are being heard in court.

"There are lots of losses that you feel over time and that cannot be made up," he said of losing his parents. "The physical loss is irreplaceable."

Videla was previously convicted in December of human rights abuses during his rule and is currently serving a life sentence in prison.

Bignone was sentenced in April of last year to 25 years in prison for kidnapping and torturing 56 people.

By the CNN Wire Staff