The drugs are known to raise levels of the male sex hormone testosterone.
A study published in the Journal of Biological Chemistry by Yale School of Medicine found high levels of the hormone killed off nerve cells.
The researchers believe the effect might explain why some steroid users become aggressive and suicidal - a condition known as hyperexcitability.
The condition is well known in the bodybuilding world, where it is referred to as roid rage.
Lead researcher Professor Barbara Ehrlich said: "Next time a muscle-bound guy in a sports car cuts you off on the highway, don't get mad, just take a deep breath and realise that it might not be his fault."
The Yale team exposed cultured nerve cells to testosterone, and found that it triggered programmed cell death (apoptosis).
This is a natural process that in normal circumstances plays a key role in clearing away damaged cells which might be harmful.
However, when healthy cells also become suicidal, it can cause severe problems, and has been implicated in neurological illnesses, such as Alzheimer's and Huntingdon's disease.
Apoptosis is characterised by membrane instability, DNA fragmentation, and the activation of "executioner proteins", known as caspases.
