A process for producing boron nitride nanotubes (BNNTs) involves providing a one or more sources of boron, nitrogen and hydrogen to a stable induction plasma to form a reaction mixture of boron, nitrogen and hydrogen in the plasma, and cooling the reaction mixture to form BNNTs. The process is capable of very efficiently producing small (10 nm or less diameter), reasonably pure BNNTs continuously in high yield at or around atmospheric pressure without the need to use metals as the catalyst. The process may be further modified by providing one or more sources of carbon to produce BNNTs doped with carbon (e.g. BCNNT).