Anita - this is oxidation and requires an oxidation chemical to remove. Oxi-Wash is a product by SoftWash Systems that is designed to remove these "gutter stripes". Bleach or pressure washing will not remove these.
There are also products such as Gutter Grenade, Gutter Zap, that work well too.
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Brandon Vaughn
All-Clean! SoftWash Gresham, OR brandon@allcleansoftwash.com www.allcleansoftwash.com 503.887.6404
Oxi-Wash also removes oxidation on vinyl siding and other surfaces too, not just gutters. It's not part of a typical house wash quote as it takes a lot more time and effort to manually agitate some surfaces to remove the oxidation, so if you add this onto your quote, price accordingly. If you use these other products that Brandon mentioned, check them out on the forums because some do not work as well in colder weather. I don't have much experience with cleaning oxidation but you should be careful how much pressure you apply as some butyl (sp?) based cleaners will remove paint that has been heavily oxidized. I don't think Oxi-Wash is butyl based..?