A total of 43 people, including at least 12 children, were killed in the May 2002 bombing.
The trial of Murad Abdurazakov and Abdulkhakim Abdulkarimov began on Wednesday behind closed doors in the Supreme Court of the Dagestan region, which borders on Chechnya.
The two are among 10 people blamed for the blast, which struck as a military band was marching in the Caspian Sea port of Kaspiisk on Victory Day, the holiday commemorating the Nazis' defeat in World War II.
The two suspects face charges of terrorism, which could bring them life sentences if they are convicted, said Seifudin Kazakhmedov, an investigator in Dagestan's prosecutors' office. A third suspect in detention is undergoing treatment in a psychiatric hospital, the ITAR-Tass news agency reported.
Abdurazakov and Abdulkarimov's alleged motive in the bombing was to instill fear in the regional police and political leadership and fuel instability in the region.
Russian officials have blamed Islamists for many attacks in recent years.
Many Dagestanis sympathise with the plight of their Chechen neighbours waging an independence struggle against Moscow.
The mountainous republic of Dagestan is home to more than 32 ethnic groups - each one with its own language.