HIV infected patients who are presumed to have neurosyphilis or have definitive neurosyphilis are treated for the neurosyphilis with either penicillin G or ceftriaxone. Patients are treated for 10 days and followed for 50 weeks after treatment. Patients receiving penicillin G are hospitalized while receiving the penicillin. Patients receiving ceftriaxone are treated on an inpatient basis for at least the first three days and may then be discharged to receive outpatient treatment. During treatment, patients are permitted to take antiretroviral drugs or other drugs for opportunistic infections except for drugs that are antisyphilitic. Lumbar punctures will be performed.