Mariano Galán Zancajo
Long hair is a recessive trait versus short hair, so to be expressed need an homozygous pair of recessive genes.
If we call "C" to the short hair gene and "c" to the long hair gene, you need a combination "cc" to have a dog with long hair, so the sire and the dam of you litter should be heterozygous "Cc" in the hair lenght locus.
What is the problem?
The long hair is a disqualifying fault in the Basset Hound. Is not a health problem, but it would be advisable not to breed with this sire or dam again.
If you use the dam or the sire in the future with other Basset Hound the most probably is that the other dog will be "CC", so you will have a litter with the next results.
In phenotype all the puppies will have 100 % short hair.
In genotype 50 % of the puppies will be homozygous "CC" and the other 50 % of the puppies will be heterozygous "Cc" and therefore they will be carriers of long hair gene and could have puppies with long hair if somebody mating this puppies with other "Cc" Basset Hound in the future.
In my oppinion, unless the sire or the dam are great dogs I will not breed with they never more.
I´m from Spain and I have any knowledge about European blood lines, and in 8 years I have seen only one Basset Hound with long hair and was a Basset Hound without pedigree.
Could be very interesting that you share with all of us the name of your dogs and perhaps could find the origin of this issue.
Sorry because English is not my native language. I hope all the people could understand what I say.

Rudy Smith
Dear Sharon, it is a simple recessive gene (allel is a better word) that gives long hair, both parents are carriers. Combined to other bassets these parents will probably only give shorthairs. Or they have to 'meet' a carrier/heterozygotic one again. So keep in mind they will still give the longhaired gene to 50% of their offspring. We prefer not to breed the 'long coats' but not a major problem in the breed. It is in the breed for decades and like all recessive genes will probably stay in the population. For those who do find it a major problem I would say: don't breed with the heterozygotes also...

It probably comes from the Clumber spaniel. But in literature you find more 'bassetised spaniels' so other spaniel breeds may be involved.