A process is described for preparing directly spinnable polymer solutions containing as fiber-forming substance polymers containing at least 95 mol %, based on the polymer, of the recurring structural unit of the formula I[--CO--R.sup.1 --CO--NH--R.sup.2 --NH--] (I)and up to 5 mol % of structural units as formed in the conversion/reaction of aromatic, aliphatic or cycloaliphatic dicarbonyl dichlorides and/or diamines. R.sup.1 and R.sup.2 are independently of each other 1,6-naphthylene, 1,7-naphthylene, 2,7-naphthylene, 3,4'-biphenyldiyl or 1,3-phenylene. The polymers prepared by reacting diamines of the formula (II) with dicarbonyl dichlorides of the formula (III) in solutionH.sub.2 N--R.sup.2 --NH.sub.2 (II)ClOC--R.sup.1 --COCl (III)The process contains the steps ofa) presenting the diamines as initial charge in the form of a solution in N-methylpyrrolidone,b) adding the dicarbonyl dichlorides to this solution,c) using starting monomers having a purity of greater than 99.9% and a water content of less than 70 ppm, measured by the method of Karl Fischer,d) polycondensing at temperatures between -20.degree. and 100.degree. C. with forced circulation of the reaction solution,e) terminating the polycondensation at a certain inherent viscosity of the polymer of at least 1.5 dl/g, measured on a 0.5% strength polymer solution in concentrated H.sub.2 SO.sub.4 at 25.degree. C., by neutralizating of the reaction solution by addition of basic alkali metal and/or alkaline earth metal salts.