Nordheim received numerous awards for his compositions, and from 1982 lived in the Norwegian government's honorary residence, Grotten, next to the Royal Palace in Oslo.

Inspired by Giovanni Gabrieli's canzone, the work showcases Nordheim's historical leanings, as well as his occupation with space as a parameter of music.

Nordheim's spatial concerns, coupled with his focus on death and human suffering, are brought together in what is arguably his most famous work, Epitaffio per orchestra e nastro magnetico (1963).

Written in memory of the Norwegian flautist Alf Andersen, who died that year at a very young age, the work incorporated Salvatore Quasimodo's poem Ed è sùbito sera.

In The Tempest, a ballet based on Shakespeare's play, electronics and orchestral sounds are again mixed, while the focus is more strongly on vocal music (e.g. the 'double voice' of Caliban), while Nordheim's continued use of historical elements is shown by the incorporation of Leonardo da Vinci's musical rebus, which solved reads Amore sol la mi fa remirare, la sol mi fa sollecita.

Based on a medieval Norwegian poem (Draumkvedet, The Dream Song), the work was composed in honor of the millennium of the city of Trondheim in 1997.