In full the Process Church of the Final Judgment. Religious cult movement that flourished in the 1970s, founded by the Englishman Robert de Grimston. It originally developed as a splinter client cult group from Scientology. The members of the group underwent a social implosion and moved to Xtul on Mexico's Yucatan peninsula, where they developed a religious theology. They believed in four gods: Jehovah, Lucifer, Christ and Satan, which were interpreted as personality types. These gods were in conflict, but the gods where about to be reconciled, at which point the world would end. They later established their base of operations in the United States.
They were often viewed as Satanic on the grounds that they worshipped both Christ and Satan; however they believed that Satan had turned from his evil ways and become reconciled to Christ, and that they were coming at the end of the world to judge humanity, Christ to judge and Satan to execute judgment. (In which regards they seem similar to the Yezidis).
Robert de Grimston was later rejected by most of the group as leader, who disliked the increasingly Satanic emphasis of his teachings. After this the group fell apart; the majority of members rejected de Grimston and went on to form the Church of the New Millennium, later called the Foundation Faith of God. This group has moved further away from the original Processean beliefs, and increasingly resembles a traditional Christian denomination. De Grimston attempted to restart the Process Church several times, but he could never replace his original following.
A detailed history of the Process Church is contained in William S. Bainbridge's book "Satan's Power". (Note he changes the name of the group and the people involved in this book, in order to hide their identity; e.g. "Satan's Power" = "Process Church", "Edward de Forest" = "Robert de Grimston", etc.)