The men are pleading not guilty to a range of charges including murder, persecution and genocide.
The trial, the largest yet staged at The Hague, is one of just a handful dealing with the killing of 8,000 Bosnian Muslims in the UN safe haven.
The massacre is the only event from the Bosnian war classified as genocide.
Five of the seven standing trial at The Hague face genocide charges, as well as crimes against humanity.
The prosecution alleges that some of the defendants were involved in the "systematic" operation to kill thousands of Bosnian Muslims and then conceal them in mass graves.
The trial opened in confusion when chief prosecutor Carla Del Ponte began to describe a visit to Srebrenica."Earlier this week I was in Potocari [near Srebrenica] to mark the 11th anniversary of the Srebrenica atrocity. I stood with thousands of mourners, mostly women..." she said, before being cut off.
Defence lawyers objected to her statement, complaining that it was "emotive", and judges ruled that Ms Del Ponte would have to wait until official opening statements before she could speak.
Although the defendants have entered their pleas, opening statements in the trial are not due until after the tribunal's summer recess.
The case was adjourned until opening statements on 21 August.
Correspondents say the case is one of the most important yet brought before the tribunal.
Just six men have so far been convicted over the Srebrenica massacre, and only two of those on genocide charges.
The two men accused of masterminding the massacre, former Bosnian Serb leader Radovan Karadzic and his military commander Ratko Mladic, remain at large.