A catalytic process for synthesis of pure, mono-crystalline alpha-Si3N4 filaments, with iron particles of some micrometres in diameter as catalyst, was investigated. Silicon subhydrides, produced in situ by reaction of silicon powder with hydrogen at 1300-degrees-C, were used as the silicon source. Experiments with molecular nitrogen as the nitrogen source failed, but the use of ammonia was successful. At 1300-degrees-C mono-crystalline alpha-Si3N4 filaments up to some micrometres in diameter and some centimetres in length were successfully produced. These filaments exhibit tensile strength values between 30 and 50 GPa, and Young’s modulus values between 550 and 750 GPa.