This study is divided into 3 sections, as follows: Part 1A is a single-dose study in neonates 0 to 72 hours of age. If four of four patients reach the minimal therapeutic level with less than Grade 3 toxicity, the ABC dose is escalated. Part 1B is also a single-dose study in infants 21 to 28 days of age, starting with the dose identified in Part 1A. If four of four patients reach the minimal therapeutic level with less than Grade 3 toxicity, the dose is escalated again. Finally, Part 2 is a multi-dose study to examine a dosing regimen for ABC and ZDV for neonates 0 to 72 hours of age. The dosing regimen for ABC is the dose defined in Part 1A for the first 3 weeks (0 to 3 weeks of age) followed by the dose defined in Part 1B for the second 3 weeks (3 to 6 weeks of age). All patients receive 6 weeks of standard ZDV therapy.