Victory Day marks the final surrender by Nazi Germany to the U.S.S.R. in WWII, often referred to as the Great Patriotic War in Russia and other states in the former Soviet Union.
Moscow's Military District Commander, Col. Gen. Valery Gerasimov, is running the parade.
Russian President Dmitry Medvedev addressed the parade, congratulating the veterans and promising "a peaceful future" for Russia.
"Any aggression against our citizens will be met with an adequate response, and the future of Russia will be peaceful," he said.
The parade, which is accompanied by a large military orchestra of 1,100 musicians, is divided into three parts - a march pass, involving military personnel, followed by sophisticated hardware and a fly over by combat aircraft.
Russia's advanced S-400 Triumf air defense systems are displayed for the first time in the parade.
This year's event is largely considered a rehearsal for a grandiose military parade in 2010, when Russia celebrates the 65th anniversary of the victory in the Great Patriotic War.
The first Victory Parade was held on Red Square on June 24, 1945 on the order of the then-Supreme Commander-in-Chief, Joseph Stalin.
Under a new law recently signed by President Medvedev, Victory Day parades involving military hardware are held this year for the first time in 23 Russian cities, rather in Moscow alone.
