I added hair particles to an object and set the view to rendered in the viewport. With Cycles the hair is rendered correctly, but with Eevee only black lines are displayed. The rest of the scene is rendered correctly with both engines.
The problem with the black lines was caused by an old graphics driver.
But the hair was still just displayed as colored lines after that.
This however was due to the render setting "Hair Shape Type" which was set to "Strand". Setting it to "Strip" as shown in the image below fixes that.