The group was formed in Gödöllő, Hungary at the end of 1995 by guitarist András Perneczky and drummer Attila Máthé. The team was soon joined by bass guitarist László Liwa who had previously played together in a local band with the founders of the group.

Initially the group's musical style was heavy metal with elements of progressive. Since the group's concept was not to go in a purely instrumental direction, but rather to produce a more eclectic style, it was essential to find a vocalist. In the absence of a lead singer they made no public appearances. The product of this period was an instrumental studio recording , which was never distributed, which is the sole trace of their music during that period. In the summer of 1997 the band was joined by vocalist Péter Budai who had also earlier been vocalist / guitarist in another Gödöllõ group.

The previous stylistic direction of the band was somewhat modified, achieving a more mainstream sound with the combination of new musical elements. Their music was grounded in experimental heavy rock / metal but with a dominant role for elements from Hungarian folk music. The English lyrics were mixed with significant excerpts from the texts of Hungarian folksongs. Metal Hammer, the biggest metal magazine in Hungary, wrote in its last issue: 'Their music could at best be described as: Tool meets dark Hungarian folk music'.

In August 1998, the band played at the 13th Annual Talent Competition in Ugod, winning a special award. The performance was given a good review in Metal Hammer' rock music magazine. In January 1999 the group recorded its first three track demo at the Honvéd studio in Budapest with the help of recording engineer Jácint Jiling.

The demo recording received good reviews from several prominent members of the national rock press: there were positive write-ups from the critics of Metal Hammer, Shock, Eclectic, Shining, Vol. 10 magazines and also some foreign (mainly German) fanzines and radio stations.

In October 1999, Aebsence won the biggest Hungarian Rock Talent Competition (called 'Eastern Ace') and played at Metal Hammer's Rock Festival. In this year the band was featured on a rock/metal compilation CD which is planned for national distribution with primarily promotional aims in mind.

In 2000 the band played several gigs nationwide for the country's metal fans. In the end of that year they were on home tour with company of Kaotika and Dying Wish, then in the next year Aebsence was on a similar circuit with bands Dark Clouds and Mood.

Beginning of 2002 they started to record their debut at the HSB and Honvéd studios, in Dunakeszi and Budapest, with producer and record engineer Viktor Sheer and Jácint Jiling. Because of financial problems the album was published at the end of that year. Just like the demo, the debut also received very good reviews from national and international magazines and webzines. It was voted the best hungarian album of 2002 by the Metal Hammer Magazine.

In march of 2003 drummer Attila Máthé temporarily left the band. During that year he resolved to leave the band for good. They played the previously confirmed shows with the help of János Moldoványi (ex-Dying Wish, Fürgerókalábak).