Bifunctional initiators for anionic polymerization are prepared by reacting an alkenylaromatic compound of the general formula I ##STR1## where Ar is aromatic hydrocarbyl which may be substituted by alkyl or another group inert toward organoalkali metal compounds and may contain nitrogen,R.sup.1 is linear or branched alkyl, cycloalkyl, alkenyl or aralkyl or from 1 to 22 carbon atoms where at least the carbon adjacent to the double bond is saturated and aliphatic,R.sup.2 is hydrogen or is likewise linear or branched alkyl, cycloalkyl, alkenyl or aralkyl or from 1 to 22 carbon atoms where at least the carbon adjacent to the double bond is saturated and aliphatic, and where R.sup.1 and R.sup.2 may be part of a common cycloaliphatic ring, in the presence of one or more ethers and of tertiary amines and in the presence or absence of a further inert aliphatic, alicyclic or aromatic solvent, at from -20.degree. to +70.degree. C. with preferably lithium and with dimerization, with the use in addition of poly-cyclic aromatic hydrocarbons which catalytically promote the dimerization in amount of from 0.001 to 50, preferably 20, mol % and with or without the removal of the ethers and/or tertiary amines after the preparation, and are used for polymerizing anionically polymerizable monomers such as styrene.