Stanisic was chief of state security services and Simatovic was commander of special operations.
They face life sentences for five counts of murder, persecution, forced deportations and inhuman acts during the 1991-95 Balkan wars.
Both have pleaded not guilty.
Prosecutors allege they set up paramilitary units such as Arkan's Tigers and the Scorpions, who rampaged through villages in Croatia and Bosnia, driving out or murdering non-Serbs.
The Scorpions gained notoriety years after the conflict when at the genocide trial of Slobodan Milosevic, the former Yugoslav president, a video was played of members of the group gunning down six Muslims captured after the 1995 fall of Srebrenica.
"The day will come in this trial when we have to watch their deaths again," prosecutor Dermot Groome said.
Simatovic was special operations chief [AP]
He said that the Scorpions were not a rogue militia or band of criminals, but "a unit that was well-trained, well-equipped, well-paid".
"They had everything they needed, including a licence to clear the land of unwanted peoples - a licence to murder," he said.
The Scorpions, he told judges, were part of a carefully planned conspiracy to ethnically cleanse regions of Bosnia and Croatia of non-Serbs by unleashing the paramilitaries.
Stanisic and Simatovic were close aides to Milosevic, who Groome described as the "driving force" behind the campaign.
Milosevic died in his cell in 2006 before the end of his trial and the case against Stanisic and Simatovic is one of the last chances for the UN court to hold high-ranking members of his regime accountable for crimes they allegedly committed.
The trial had been postponed four times in recent weeks amid concerns about Stanisic's health.
Doctors had warned that Stanisic was too ill to attend his trial and the case "could harm the health of the accused".
|Stanisic was chief of state |
security services [EPA]
But Patrick Robinson, the presiding judge, said the trial could start, adding that Stanisic's condition would be closely monitored.
Stanisic's lawyer, Geert-Jan Knoops, said having a defendant watch proceedings via video from a cell block was unique in international law and told Judge Robinson that he would ask court officials Tuesday to clarify his position as Stanisic's lawyer and said he could withdraw from the case.
He argued the video link will hinder his ability to defend Stanisic.
"Physically, you need to have a client who is capable of giving you clear instructions and that is not the case now," Knoops said outside the court.
The court is under pressure from the UN Security Council to finish all its trials by 2010.