A 17-year-old boy from London, an 18-year-old man from Portsmouth and a 21-year-old man from Bath were arrested in pre-planned operations today, the North East Counter Terrorism Unit said.
The arrests came in an investigation into a neo-Nazi group called Sonnenkrieg Division, it is understood.
Detectives are continuing to look for evidence in four properties in Leeds, Bath, London and Portsmouth.
The North East Counter Terrorism Unit said it was not disclosing where in Leeds the property being searched was.
The oldest suspect was arrested on suspicion of possessing material useful to someone preparing an act of terrorism and conspiracy to inspire racial or religious hatred.
The youngest suspect was detained on suspicion of encouraging terrorism, disseminating terrorist publications and conspiracy to inspire religious or racist hatred.
The 18-year-old was arrested on suspicion of encouraging terrorism and disseminating terrorist publications.