PURPOSE: To provide a process for giving silica-alumina fibers excellent in spinning stability, mechanical strength and heat resistance.

CONSTITUTION: An alkylaluminum or a combination thereof with a silicon- containing compound and/or a β-diketone of the general formula: R1COCH2COR2 (R1 and R2 are each an alkyl or an alkoxy group) are mixed with an organic solvent containing 0.9-1.4 mole of water per mole of the alkylaluminum to effect bydrolysis. To the hydrolyzate, an alcohol of the general formula: R3OH (R3 is an alkyl group) is added, and as necessary, a silicon-containing compound and/or a β-diketone are further added thereto and they are adjusted so that the amount of the β-diketone becomes 0.03-0.2 mole per mole of the aluminum in the mixture, the alcohol becomes more than 0.8 mole per mole of the aluminum, and the silicon-containing compound corresponds to less than 40wt.% in the silica-alumina fibers. Then, the adjusted mixture is subjected to the spinning process.