I have the same dark circles under the eyes.
I read that they indicate liver problems.
Maybe Andreas has some more specific information, like if doing a series of liver flushes will help to eliminate them.

I used to have really dark rings under my eyes until i got into the habit of drinking more water more regularly. I try to have 2 liters a day and ever since the circles are gone.....

Lisa,

These relate to kidney and liver congestion. Dehydration and eating concentrated protein foods, such a meat, fish, eggs, poultry, and cheese, and common causes. Going to bed too late (way after 10pm) affects both the liver and kidneys and can also cause the dark circles. THe liver is in charge of removing toxins and noxious substances from the blood, but if the bile ducts are clogged up, these substances remain in the blood. Some of them enter the kidneys and affect them negatively. Others accumulate in the connective tissues under the skin, most visible where the skin is very thin, for example, under the eyes. Dehydration is another common cause. He should drink 6-8 glasses of water per day and avoid drinking diuretics like coffee, cokes, and other soft drinks/power drinks.

Andreas