While mainly focused on playing the guitar and developing a language of improvisation, Björkenheim has also maintained a keen interest in composing. His first commission to write for big band in 1982 was the beginning of a career composing for big band, symphony orchestra, string quintet, electric guitar orchestra, and small jazz ensembles. Click HERE to go to a page with a list of main compositions, where you can also take a look at the scores themselves. He has also composed and recorded the scores for ten films.