Questions arise about the constitutionality of including some form of prayer, usually an invocation or benediction, in public school graduation ceremonies, and whether such prayer can appropriately be delivered by a minister or other religious leader. The U. S. Supreme Court has not addressed this precise issue, but an analysis of other courts' decisions, and related Supreme Court precedents, may help educators to assess the factors involved in assessing the constitutionality of this widespread practice. Arguments against prayer at graduation ceremonies are based on the Establishment Clause of the First Amendment that reads: "Congress shall make no law respecting an establishment of religion...." An examination of the cases cited indicates that the outcome of a commencement exercise challenge appears to hinge on the evidence of school district involvement designed to advance religious purposes. Without aggravating circumstances, a court would seem to be unlikely to find an Establishment Clause violation in the context of the traditional ceremonial nature of commencement exercises. (Thirty-two references) (MLF)