Alksnis is the grandson of the repressed Soviet military leader Yakov Alksnis. He was born in the Kemerovo region, where his family was exiled, and after rehabilitation, he and his parents returned to Riga. He graduated from the Riga Higher Military Aviation Engineering School named after his grandfather and served in the Baltic Military District.
In 1988, he began his political career, initially advocating for the expansion of Latvia's sovereignty within the USSR, and later opposing its independence restoration. In the autumn of 1991, he was expelled from the Supreme Council of the republic for not resigning from the Soviet army. During the 1990s, he was involved in pro-Soviet and right-wing organizations in Moscow and participated in the founding of the Russian People's Union.
During the conflict between President Boris Yeltsin and the Supreme Council, he organized anti-presidential protests, during which he was brutally beaten by OMON. In 2000, he was elected to the State Duma, actively supporting pro-Russian separatists in the former USSR and publicly advocating for Crimea's separation from Ukraine. He criticized Russian President Putin from a right-wing perspective: "Remember my words: the damage that Putin is inflicting on Russia today will far exceed the damage done by Gorbachev and even Yeltsin."
He himself held eclectic views, opposing ethnic nationalism and communism while enjoying support from right-wing politicians and Stalinists.
As a deputy in the State Duma, Alksnis became embroiled in one of the first public scandals in Russia related to the blogosphere. He attempted to prosecute a blogger who called him a "patented star-bearing m***k" on the social network LiveJournal.
In his response, he referred to himself as a "Category A official," a phrase that briefly became a popular internet meme. He was a trusted representative of the Communist Party of the Russian Federation's presidential candidate Pavel Grudinin and supported the political ambitions of Igor Strelkov (Girkin).