His recordings and performances have typically alternated between jazz and chamber or opera music, the latter often in collaboration with his father, composer Karlheinz Stockhausen.

At age four he appeared as "child at play" in his father's theatre piece Originale.

In November 2008 he gave the first performance of Freedom Variations, a composition for trumpet and chamber ensemble written by Italian composer Lorenzo Ferrero.

[3] The Markus Stockhausen Group (with Jeroen van Vliet p, Christian Thomé dr, Jörg Brinkmann cello) released on 27 August 2021 the album Tales.

[4] [6] With Rainer Brüninghaus With Ralph Towner With Lebowski With Gaspare Bernardi