[15] On 27 December 1979, Soviet leader Leonid Brezhnev launched a surprise armed intervention and regime change operation in the Democratic Republic of Afghanistan.

[16] According to Russian sources, the members of this highly trained group performed remarkably well, losing only two men; the lightest casualties of any of the forces involved in the raid.

On-site analysis of the area was conducted by Airborne deputy commander Alexander Lebed, and other senior officers who mingled with the crowds of anti-coup protesters nearest to the White House.

There was a general consensus among the military officials who gathered that day, as evidenced by their statements months after the botched coup attempt, that had they followed through on their endeavour it would have succeeded.

[26] Shortly after their assessment was made, Gen. Karpukhin and Vympel's Boris Beskov convinced the KGB Deputy chairman, Gennady Ageyev, that such a massive undertaking should be cancelled.

[5] As part of the government shakeup following the June 1995 Budyonnovsk hospital hostage crisis in which the Alpha Group had a leading role, Yeltsin fired the first Director of the Federal Security Service (FSB), Sergei Stepashin.

[5] Meanwhile, Alpha veterans became active in legitimate businesses (such as the private security company Alpha-B co-founded by Col. Golovatov in August 1993[31]) in organised crime, as well as in politics.

[8][34] In December 1997, Alpha freed the Swedish trade counsellor Jan-Olof Nyström who was kidnapped in Moscow by a gunman similarly demanding a ransom and a flight out of Russia.

[37] When one of the Alpha troops, Lt. Sergeyev, who was near the White House, was mortally wounded by sniper fire from the nearby Hotel Ukraina, the unit finally agreed to move.

[37] Opposition gunmen were blamed for the shooting, but it is possible that the shots were actually fired by members of a special unit loyal to Yeltsin; it was rumoured that the snipers in the hotel were commanded by Alexander Korzhakov, chief of the Presidential Security Service (SBP).

[37][38][39][40] In the end, Rutskoy and the other leaders of anti-Yeltsin faction, including Ruslan Khasbulatov, Vladislav Achalov and Viktor Barannikov, all negotiated their surrender to the Alpha troops, who had entered the shelled and burning building after the shooting stopped, and brought them, along with the detained Supreme Soviet deputies, to Lefortovo Prison.

[8] In August 1996, when the city was retaken by Chechen separatist forces, 35 of them (including 14 members of the territorial Alpha unit from Krasnodar Krai)[8] took part in a defence of the FSB headquarters.

By the war's final ceasefire, the main FSB office was one of the few key structures still being held by federal forces in central Grozny, but at the cost of 70 of its defenders' lives in some of the fiercest fighting during the last battle.

[43][44] Allegations arose, following the Khasavyurt Accord of August 1996, that the ATC carried out clandestine operations intended to discredit the Chechen Republic of Ichkeria, so that it would not receive international recognition of its independence.

[45][46][47][48] It is believed that the SSGs were behind many of the numerous "name/address cleansings" (imeny/adressny zachistki): usually night-time raids by masked men in unmarked vehicles, targeting specific active or former rebel combatants, their supporters, their relatives, or other civilians for either forced disappearance or outright extrajudicial killing.

At Budyonnovsk (Budennovsk) in Stavropol Krai, two abortive storming attempts by Alpha and Vympel killed scores of hostages in a major public relations disaster for the Russian government, as the carnage was televised live across the country.

[52] After that, the leader of the hostage-takers, Chechen commander Shamil Basayev, agreed to release pregnant and nursing women, and to allow emergency services to put out a fire in the main building and to collect and remove dead bodies.

[5] In the end, the crisis was resolved through negotiations that led to an agreement involving a ceasefire in Chechnya and high-level peace talks, both of which later broke down, with full-scale hostilities resuming in October 1995.

[53] At Pervomayskoye, a small settlement on the outskirt of Kizlyar in Dagestan, in an operation that was conducted under the direct control of Barsukov, Alpha Group was mostly held in reserve during multiple failed storming attempts spearheaded by Vityaz and the SOBR (a special forces unit of the Moscow police), supported by tanks and armoured vehicles.

[51] According to statements made to justify the use of unlimited force, the FSB had been informed, falsely, that the hostages had been executed by their captors, prior to the commencement of military operations.

[51] This full-scale offensive continued for three days, until the Chechen militants fought their way through the siege lines in a night-time break-out, escaping with many of the surviving hostages in another major humiliation for the Kremlin.

[51] Although they avoided the kind of devastating losses that decimated the Moscow SOBR (including the death of their commanding officer)[12] and the 22nd Independent Brigade of Spetsnaz GRU,[54] Alpha Group still suffered casualties at Pervomayskoye.

One of these actions was the use of an unknown chemical agent to assist Alpha Group and the SOBR break the October 2002 Moscow hostage crisis, by knocking out the people inside the building.

On 3 September 2004, the local school was taken over by Chechen-led militants from Ingushetia, and was subsequently raided by the heavily armed FSB special forces of Alpha and Vympel.

John McAleese, a member of the Special Air Service (SAS) team which had liberated the Iranian Embassy in London in 1980, immediately called it one of the worst hostage rescue attempts he had seen or heard about.

[69] In 2006, five members of Arystan were arrested and charged with the kidnapping of the opposition politician Altynbek Sarsenbayuly, his driver, and his bodyguard; the three victims were then allegedly delivered to the people who murdered them.

In 1995, members of Alpha and the Minister of State Security, Igor Giorgadze, were blamed for the failed bombing attempt on the life of President Eduard Shevardnadze.