Her first band, also named "Alex", was formed in 1976 together with Bjørn Christiansen, Svein Gundersen (from the earlier noted Rock group Aunt Mary), Brynjulf Blix and Per Ivar Johansen.
In addition to performing all over the world, Alex was also given her own television special in the German Musikladen series, which was viewed by 20 million people in over 18 countries worldwide.
During the early 80s, Naumik took part in Melodi Grand Prix, the Norwegian national finals of the Eurovision Song Contest, on four occasions, with her third place in 1980 as her best result.
Following the peak of her popularity in the mid-80s, Naumik gradually turned to producing records and writing material for other artists, spending several years working in both the United States and Japan, before returning to Norway in the early 2000s.
Her most recent success was her work with Swedish-born artist Leana's album Faith, which reached number one on the Billboard charts in June 2006 and January 2007.