After the second washout, patients will begin combination therapy with capravirine plus at least two other anti-HIV medicines. (These may include a reverse transcriptase inhibitor such as zidovudine, didanosine, lamuvidine, zalcitabine, or stavudine, and maybe one or more protease inhibitors such as ritonavir, nelfinavir, saquinavir, indinavir or amprenavir.) For the first week, patients will have a daily blood test to determine HIV blood levels. Afterwards, treatment will continue on an outpatient basis with clinic visits every 4 to 8 weeks for physical exams, lab tests and other procedures as required. The study will last approximately 48 weeks. Patients who benefit from capravirine therapy may be able to continue to receive the drug from the drug company sponsor or as part of another study, or the protocol for this study may be amended to lengthen the treatment period.