This research is being done to find out if Baclofen, a medicine that is often used for the treatment of abnormal stiffness, might also be useful to treat some of the neurologic problems caused by ataxia telangiectasia (A-T). The investigators also want to find out if there are better ways to measure the problems of ataxia and abnormal eye movement for future studies of medication in ataxia telangiectasia.

Inclusion Criteria:

• Teenagers over 12 years old and young adults with A-T may join if they have been evaluated previously in the A-T Clinical Center at Johns Hopkins Hospital and have a measurable abnormality of eye movement.
• Patients who are presently taking Baclofen will be eligible for the study if they are presently receiving the medication under the direction of Dr. Crawford in the ATCC, and are willing to withdraw from the medication for a period of one month prior to the initial screening visit.
• Female patients who are sexually active will be given a standard serum HCG pregnancy test.
• Those who are sexually active will be counseled about necessary precautions against pregnancy during the duration of the trial.

Exclusion Criteria:

• A positive pregnancy test.