1. A process for the production of optionally branched polyarylene sulfides of a) 50 to 100 mol-% aromatic dihalogen compounds corresponding to the following formula see diagramm : EP0215259,P7,F1 and 0 to 50 mol-% aromatic dihalogen compounds corresponding to the following formula see diagramm : EP0215259,P7,F2 in which the X's represents halogens, such as chlorine, or bromine, in the meta- or para-position to one another, the R**1 's may be the same or different and represent hydrogen, alkyl, cycloalkyl, aryl, alkylaryl, arylalkyl ; two substituents R**1 in the ortho position to one another may be attached to form an aromatic or heterocyclic ring and one substituent R**1 is always different from hydrogen and b) 0 to 5 mol-%, based on the sum of the aromatic dihalogen compounds corresponding to formulae I and II, of an aromatic tri- or tetrahalogen compound corresponding to the following formula ArXn in which Ar is an aromatic or heterocyclic radical, X is halogen and n is the number 3 or 4 and c) 50 to 99 mol-% sodium or potassium sulfide and 1 to 50 mol-% sodium or potassium hydrogen sulfide, the molar ratio of (a+b):c being from 0.75:1 to 1.15:1, in d) an organic solvent using catalysts and/or cosolvents, the molar ratio of sulfide and hydrogen sulfide c) to the organic solvent d) being in the range from 1:2 to 1:15, characterized in that the optionally continuous reaction is carried out by adding the solvent, the aromatic halogen compounds of formulae I, II and III and the hydrogen sulfides and sulfides with the catalysts and/or cosolvents in anhydrous form simultaneously or successively to the reaction mixture, solids used having a particle size in the range from 1 to 5000 micrometers.
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