Maybe it's from spider mites. Can you sometimes see little string- or web-like filaments between the branches or among the leaves? I had similar-looking damage on my pepper plants and resolved the problem with a neem oil spray.

Hi roscaalcamo, I used neem oil like you suggested and it already seems to be working! Thanks so much, I think you might have saved my peppers!

That does not look like a Spider Mite problem to me, more like Early Blight.

Here is a link that might be useful: About Early Blight