one, you might have trees above that section leaching or sweating out sap and this gets cooked by the sun and discolors and then runs. If this is the problem, remove the branches, and allow the sun to bleach out the stains or there is a wash that might work, Bleach will work also, but can harm plants below.
two, you could have mineral deposits in the comp shingles that are actually rusting. The chat used on comp shingles sometimes get contaminated with minerals that act like metals and rust and leave long trailing stains. This cannot be fixed as it will only come back. If the roof is relatively new and you have the receipt you can with some patience get new shingles from perhaps owens corning. But you do have to pay for rip off and re install.
had a roofer tell me this an I closely inspected this and found it to be true.