WASHINGTON — A bitter personal struggle between two powerful figures in the world of terrorism has broken out, forcing their followers to choose sides. This battle is not being fought in the rugged no man’s land on the Pakistan-Afghan border. It is a contest reverberating inside the Beltway between two of America’s leading theorists on terrorism and how to fight it, two men who hold opposing views on the very nature of the threat.

On one side is Bruce Hoffman, a cerebral 53-year-old Georgetown University historian and author of the highly respected 1998 book “Inside Terrorism.” He argues that Al Qaeda is alive, well, resurgent and more dangerous than it has been in several years. In his corner, he said, is a battalion of mainstream academics and a National Intelligence Estimate issued last summer warning that Al Qaeda had reconstituted in Pakistan.

On the other side is Marc Sageman, an iconoclastic 55-year-old Polish-born psychiatrist, sociologist, former C.I.A. case officer and scholar-in-residence with the New York Police Department. His new book, “Leaderless Jihad,” argues that the main threat no longer comes from the organization called Al Qaeda, but from the bottom up  from radicalized individuals and groups who meet and plot in their neighborhoods and on the Internet. In his camp, he said, are agents and analysts in highly classified positions at the Central Intelligence Agency and Federal Bureau of Investigation.

If Dr. Hoffman gets inside organizations  focusing on command structures  Dr. Sageman gets inside heads, analyzing the terrorist mind-set. But this is more important than just a battle of ideas. It is the latest twist in the contest for influence and resources in Washington that has been a central feature of the struggle against terrorism since Sept. 11, 2001.