Dark streaks down your gutters and downspouts tell us that the water is overflowing. This can be caused by several conditions 1. Downspout clogged 2. Slope of the roof is too steep and shoots the water over the gutter 3. Gutters are not attached securely to the fascia and the drop is incorrect not allowing the water to move toward the downspout. Most often it is due to clogged downspouts, either way maintenance on your gutters are a tri-yearly chore if you want to control the water successfully.
See photo below...

If water is shooting over your gutters you can install a diverter. Often times the volume of water from a heavy rain can not be captured successfully by the gutter where two or more steep roofs come together without a diverter.