Ann,

Unless this drainage from your dog's eyes is a result of some type of infection, you are most likely dealing with a fairly common problem seen in dogs with light-colored hair.

If the drainage is pus-colored (yellowish-green) or if there is a lot of redness to the "whites" of the eyes, you should have your dog examined by your veterinarian in order to establish a cause and possible treatment.

However, if the drainage is more watery and is mainly staining the hair below each eye, you are more likely seeing the chronic result of what the tears can do to light-colored hair.  I covered this topic in a past issue of my blog and you can read it at:  www.questionsondogsandcats.blogspot.com/search/label/facial hair staining

There several products available over-the-counter for this staining and I provided a reference to one of them in my blog article. 

Helpful Buckeye

Tear staining is common in Bichons and many other breeds. It just shows more on the white breeds.

Although it can be caused by an eye defect, it is generally caused by allergies, poor diet or health problems. Many puppies have it but outgrow it. Have your vet take a look.

This is not merely a cosmetic problem. Fix the cause and the symptoms will clear up.  I've written extensively about this at http://www.dogs4dogs.com/Tear%20Stains.html