"New Evangelicalism" was created during the middle of the twentieth century after the end of WWII. The term refers to those within Evangelicalism who want a "dialog" with those who reject the Fundamentals of historical Christianity. It represents a breaking off from Fundamentalism, which still adheres to the doctrines of Biblical Separation and Christian Militancy.
New Evangelicals have been at the forefront of the "Ecumenical Movement" - a movement to unify "Christendom" (Protestants, Baptists, Catholics and others) together with Muslims and other non-Christians from various religions of the world.
Three of the most notable Baptist New Evangelicals of this day are Billy Graham, Rick Warren, and Jerry Falwell. The late Jerry Falwell was a member of a subgroup within New Evangelicalism called "Pseudo-Fundamentalism".
Before New Evangelicalism was created, "Fundamentalism" and "Evangelicalism" were terms often used interchangeably to describe those who stood for Jesus and the Bible and against Popery and other sins. New Evangelicalism will probably culminate with the rise of the Antichrist with his Great Whore as foretold in the Bible in Revelation.
Nevertheless, one day very soon, Jesus will come back to the Mount of Olives and destroy the rebels. He will then set up His Kingdom in Jerusalem. Even so, come Lord Jesus!