Single crystalline mullite fibres, which are expected to be an excellent reinforcement for high temperature composite materials, can be produced by using the internal crystallisation method. The present paper sheds light to mechanisms of crystallisation of mullite fibres under conditions of the internal crystallisation method, which is actually crystallisation of a melt in the continuous channels of a molybdenum carcass. Mullite occurs to appear close to 2:1 composition independent of the composition of the melt. Inclusions of a silica-based glassy phase are also present on the periphery of a fibre. The glassy phase yields a decrease in the creep resistance of mullite fibres at temperatures above 1500°C. Still, the fibres obtained from the raw material with the Al 2 O 3 /SiO 2 molar ratio of 2.05 have excellent creep resistance at a temperature of 1400°C and fairly high creep resistance at 1500°C.