The present invention relates to a soluble polyfunctional vinylaromatic copolymer improved in heat resistance, resistance to thermal decomposition, solvent solubility, and processability. The soluble polyfunctional vinylaromatic polymer is obtained by cationically polymerizing, at a temperature of 20 to 120.degree. C., one or more monomer ingredients including 20 to 100 mol % divinylaromatic compound (a) in the presence of a donor ingredient, e.g., a quaternary ammonium salt, with the aid of a Lewis acid catalyst and an initiator represented by the following general formula (1) ##STR00001## wherein R.sup.1 represents hydrogen or a monovalent C.sub.1-6 hydrocarbon group; R.sup.2 represents an aromatic or aliphatic hydrocarbon group having a valence of p; Z represents halogen or C.sub.1-6 alkoxy or acyloxy; and p is an integer of 1 to 6; provided that when two or more R.sup.1's and Z's are present per molecule, they may be identical to different from each other.