In her opening statement, chief UN war crimes prosecutor Carla Del Ponte said the accused were among the "most responsible" for the slaughter in the eastern Bosnian town.
But she condemned Serbia for allowing top suspect Mladic to remain at large.
"This trial is an important step... These seven men, serving under Mladic and (his aide general Zdravko) Tolimir, are the most responsible for the crimes committed in Srebrenica," Ms Del Ponte said.
In the biggest joint trial at the The Hague-based International Criminal
Tribunal for the former Yugoslavia (ICTY), five of the accused face charges of genocide as well as war crimes and crimes against humanity. All have pleaded not guilty.
Ms Del Ponte said prime suspect Mladic, the Bosnian Serb military commander during the 1992-1995 war, was "inexcusably" absent from the list of defendants.
"Mladic should be on trial for this case. The inexcusable refusal by the Serbian authorities to arrest Mladic ... and hand him over means that there will be another Srebrenica case when he is arrested," Ms Del Ponte said.
"The government of Serbia is perfectly capable of doing so... It is scandalous," she said.
Mladic, Tolimir and their former political master, wartime Bosnian Serb president Radovan Karadzic, are still on the run 11 years after the massacre.
"But make no mistake: Mladic, Tolimir, Karadzic, they will be arrested and this is our pledge to the international community and to all victims and survivors," said Ms Del Ponte.
Serbia rejects charges
Serbia has rejected the accusations and vowed to capture Mladic soon.
"It seems to me that the accusation is related to a period in the past," Rasim Ljajic, the Serbian government official in charge of cooperation with the Hague-based court said.
"There is a political will and readiness and I hope that the action plan will give results soon," Ljajic told Beta news agency.
Last month the Belgrade government adopted an action plan aimed at locating and arresting remaining war crime suspects, notably Mladic, whose capture has become a key condition for negotiations on country's closer ties with the EU.
Serbian Prime Minister Vojislav Kostunica's top party official, Andreja Mladenovic, echoed Ljajic's words, saying in a separate statement that Serbia was "doing its best at this moment".
"As soon as Mladic and other fugitives are located, they will be arrested and handed over" to the UN court, Mr Mladenovic said.
About 8,000 victims were summarily executed at several locations around Srebrenica. Lightly armed Dutch peacekeepers protecting the enclave failed to prevent the onslaught, citing limited rules of engagement.
Thousands of victims have been exhumed from about 60 mass graves, and more than 2,500 have been identified by DNA analysis. Forensic experts believe more graves have yet to be discovered.