The invention relates to a reactor and to a method for continuous polymerization, in which said reactor for the continuous production of polymers, particularly synthetic rubbers, contains at least one substantially tubular reactor housing (4), wherein said reactor housing (4) has a drive shaft (30) that is connected to at least one agitator (38) arranged such that it can rotate inside the reactor housing (4), and the agitator contains at least one, and preferably two, three or four helical mixing elements (24) which are designed to be preferably close to the wall or to come into contact with the wall.