Usually it is not necessary to wait for Prozac to completely clear out of the body before starting a new antidepressant. In severe cases of depression this would in fact be a bad idea. However if the new drug is a tricyclic antidepressant (Elavil, Sinequan, etc.) or an MAOI (rarely used these days) than it is very important to wait several weeks for the Prozac to clear out because the long-half life increases the likelihood for potentially lethal interactions in the cases above.