This chapter discusses the experimental observations of magnetism in Carbon and Boron Nitride nanostructures and presents an overview of Carbon and Boron Nitride Nanotubes. The C60 anion is present in any batches of C60 and can be observed by electron paramagnetic resonance (EPR). The high electron affinity makes C60 a good radical scavenger which means it, can attract and bond to free radicals. The chapter presents the Illustration of a sheet of graphene, a zigzag carbon nanotube and an armchair carbon nanotube. Boron nitride (BN) nanotubes, which have the same structure as Single‐walled carbon nanotubes (SWNTs), provide an interesting alternative for developing electronic devices because their electronic properties, such as the band gap, do not depend on tube diameter, tube length, or chirality. The first prerequisite for the existence of ferromagnetism is the existence of unpaired electron.