 Nyorera kupfuurira kweiyi ndima - Alpha yaive ichishanda panguva yeChipiri Chechen Hondo iyo yakatanga muna 1999, pamwe nekumukira kwakatevera muNorth Caucasus. Mukati me 2000 Hondo yeKomsomolskoyeVaAlfa snipers vakabatanidzwa kuWestern Group yaVladimir Shamanov yemauto emubatanidzwa, vakaiswa mukuyedza kudzvinyirira vaSniper vaRuslan Gelayev mumusha. Sekureva kwevakuru vechikwata ichi, mashandiro ayo Alpha akapinda nawo akatungamira mukusungwa kwemutungamiriri weChechen Salman Raduyev muna 2000, kuurayiwa kwemutungamiriri weChechen Arbi Barayev muna 2001, kuurayiwa kweMutungamiri weChechen Aslan Maskhadov muna 2005, uye kuurayiwa kwemutungamiri wevapanduki vekunze Abu Hafs muDagestan muna 2006. Zvichitevera kuendeswa kwemabasa muChechnya kubva kubazi rezvekudzivirirwa kuenda kuFSB muna Ndira 2001, uye pamberi pe Chechenization mutemo wakatanga muna 2003, nhengo dzeAlpha pamwe nevamwe vashandi veRussia nemasoja eChechen pro-Moscow vakapinda mune angangoita gumi akasanganiswa mapoka akakosha akasanganiswa , SSGs, anoonekwa semapoka erufu nemapoka anorwira kodzero dzevanhu nevanoona vekunze. Zvinotendwa kuti maSSG aive kumashure kweakawanda e mazita kero yekuchenesa imenyadressny zachistki: kazhinji husiku husiku nevarume vakapfeka zvipfeko mumotokari dzisina kunyorwa, vachitarisa varwi vanopandukira kana vekare varwi, vatsigiri vavo, hama dzavo, kana vamwe vanhuwo zvavo kuti vanyangarike nechisimba kana kuurayiwa kunze kwemutemo. Muna 2005, sangano reHuman Rights Watch rakataura kuti kunyangarika kwacho kwakanga kwasvika pamwero wemhosva dzinopesana nevanhu, uye kuti Russia ine mukurumbira usina kunaka wokuva mutungamiriri wepasi pose panyaya yokunyangarika kwevanhu. UFSB yeChechnya yakaumbawo chikwata cheAlpha chemuno, icho chaifungidzirwa kuti chakafanana nebasa rayo nemaSSG. 