A continuous process for the preparation of polymer compositions having low volatile content which comprises passing a styrene polymer-containing polymerization fluid composition obtained by solution polymerization or bulk polymerization through a volatile component separator comprising vertical foaming preheaters and vacuum vessels directly connected therewith and thereby removing volatile components continuously from the polymerization fluid composition in three stages to obtain a polymer composition having low volatile content, the process being characterized in that each of the three stages includes at least one vertical foaming preheater and one vacuum vessel, the first stage is carried out under such pressure and temperature conditions that the polymerization fluid composition leaving this stage contains said styrene polymer in an amount of 60 to 80% by weight and the temperature of the polymerization fluid composition passing through this stage lies between 70.degree. and 120.degree. C., wherein the pressure within the vacuum vessel of said first stage is kept in the range of 80 to 300 Torr, the second stage is carried out in such a way that the molten polymer composition leaving this stage has a volatile content of 0.3 to 1% by weight, and can retain good fluidity, the temperature of the polymerization fluid composition heated in the preheater of this stage lies between 160.degree. and 250.degree. C., and the pressure within the vacuum vessel of this stage is kept in the range of 30 to 100 Torr, and the third stage is carried out in such a way that the temperature of the molten polymer composition heated in the preheater of this stage lies between 190.degree. and 260.degree. C. and devolatilization is effected at a pressure of 50 Torr or less in the presence of a highly volatile foaming agent.