The first experimental observation of free induction decay signals of free radicals is reported. The signals were observed on the line of the rotational transition of OH radicals in the terahertz region. OH radicals were generated by the chemical reaction of excited oxygen atoms with water molecules. Radicals were excited by free-electron laser radiation pulses. Free induction decay radiation was detected in real time using ultra fast terahertz radiation detectors. The possibility of using free induction decay signals of radicals as a new method for detection of free radicals in combustion processes is discussed.