PURPOSE: To obtain the titled oligomer, having a low melting point, and suitable as a hardener for epoxy resins, by mixing an α-methylsytrene with a conjugated diene hydrocarbon and/or a low-boiling compound, and feeding the resultant mixture in a diluted state to molten maleic anhydride under agitation.

CONSTITUTION: A mixture of an α-methylstyrene of formula II (R is H or 1W4C alkyl (at the m- or p-position) and if necessary styrene with a conjugated diene hydrocarbon compound of formula III or IV (R1 and R2 are H, CH3 or C2H5) and/or a low-boiling compound is slowly fed to a maleic anhydride of formula I (R1' and R2' are H or 1W3C alkyl) which is agitated in the molten state, and the resultant reaction solution is reacted while kept at 100W200°C to suppress the single oligomer, e.g. dimer of the α-methylstyrene, causing the deterioration in quality of epoxy resins and afford the aimed low-melting acid anhydride cooligomer suitable for the above-mentioned uses.