They propose a future antichrist, the beast. The Catholic Church also does not believe in a Kingdom Now doctrine of the world becoming better and better through the agency of the church, but adamantly deny it:
Par. 675 "Before Christ's second coming the Church must pass through a final trial that will shake the faith of many believers. The persecution that accompanies her pilgrimage on earth will unveil the 'mystery of iniquity' in the form of a religious deception offering men an apparent solution to their problems at the price of apostasy from the truth. The supreme deception is that of the Antichrist, a pseudo-messianism by which man glorifies himself in place of God and of his Messiah in the flesh."
The Catholics have long believed in a "Peter the Roman" who will be an "Angelic Pope" and lead the church through the Great Tribulation to come.
Par. 677 "...The kingdom will be fulfilled...not by a historic triumph of the Church through a progressive ascendancy, but only by God's victory over the final unleashing of evil, which will cause his Bride to come down from heaven...."