Yes, there was a large music underground in the former GDR. It formed as a direct consequence of music being heavily controlled and censored by the GDR leadership.

To understand this better one has to know that in order to release an LP a band had to do this through the offical label of the GDR, Amiga. To play their music a band also needed an official Spielgenehmigung, basically a sort of license allowing them to perform.

Now if your lyrics went through the censors check and everything was fine (read as: no politically critical content) you could play almost any type of music live and record an LP in the GDR. To my knowledge, only Punkrock or Thrash Metal were very much frowned upon by party officials due to their aggressive nature. Hardrock and Heavy Metal on the contrary were okay as long as they did not convey a political message, so that bands like Prinzip could find moderate success even in a socialist country like the GDR.

On the other hand, if you were in a band that played music that was frowned upon or with an anti-socialist lyrical theme, officials could revoke your Spielgenehmigung. This basically instantly pushed you into what was known as 'Die anderen Bands' (The other bands), essentially the musical underground.

Notable examples of the underground music scene would include:

Feeling B (Punk, later became Rammstein) Dritte Wahl (Punk) Die Skeptiker (Punk) Schleim-Keim (Punk) Macbeth (Metal) Rochus (Thrash) Rosengarten (Goth-Rock)

There also was a lot of underground activity in the singer-songwriter community (known as Liedermacher) who often cleverly disguised political messages in their lyrics to get past the officals.