Several antidepressant drugs, including Prozac, work well in battling depression. The goal of drug therapy is to treat the illness and handle its symptoms so the afflicted person will feel well enough to resume a normal daily routine. Although antidepressants are much safer than their predecessors introduced in the late 1950s, about 30 percent of patients are immune to their effects. Even for those who are not, it usually takes two to four weeks before the symptoms begin subsiding.