This study is designed to evaluate BeneFIX infused as prophylaxis regimens, compared with BeneFIX administered as an on-demand regimen only. In the trial, subjects will participate in 4 study periods. The first period is a 16-week on-demand treatment, during which subjects will utilize BeneFIX to treat bleeding events episodically only as they occur (i.e., on-demand treatment). At the end of this period, subjects will be randomly assigned to 1 of 2 BeneFIX prophylaxis regimens: either 100 IU/kg once weekly or 50 IU/kg twice weekly, and followed for 16 weeks. At the end of this period, subjects will use on-demand treatment for 8 weeks. The purpose of this 8-week period is to mitigate the potential carry-over effect of the prior prophylaxis regimen on bleeding frequency. Following this 8-week on-demand treatment, subjects will cross-over and receive the alternate study prophylactic regimen for 16 weeks.