The band's lineup was finally completed in 1984, when new vocalist Kostya Kinchev (real name Konstantin Panfilov) and guitarist Petr Samoylov joined.

Alisa toured through Europe and Israel together with fellow Russian heavy metal band Aria.

The album Black Mark, released in 1994, was dedicated to the memory of Chuma, who committed suicide by jumping from a window.

In the new millennium, with albums such as Seychas Pozdnee Chem Ty Dumaesh (It is Later Than You Think, 2003) and Izgoy (Exile, 2005), Alisa's sound became heavier.

Kinchev's fairly conservative religious-patriotic shift was viewed unfavourably by some old fans that liked Alisa for their original "rock" message.