One way to reduce the increasing waste streams of used polymers is an efficient material recycling. This requires a technology for the separation of polymer mixtures into different material fractions. For this purpose the principal suitability of laser-induced breakdown spectroscopy was investigated. Plasma emission spectra of LDPE, HDPE, PP, PET, PVC, and PS were studied. Basic investigations were performed in order to assess the influence of different measurement parameters and to optimize the analytical performance. More than 140 spectra lines are identified, which can be related to C, H, O, N, C2, CN and CH from the bulk material and the atmosphere and to Al, Ca, Cu, Fe, Mg, Sn, Ti and Zn from additives of the polymer. Estimated detection limits of down to 2 ppm are achieved for metallic additives. Different artificial neural networks were tested for the evaluation of the spectra. PET and PVC can be identified unambiguously detecting the characteristic elements oxygen and chlorine. For plastics, which differ in their contents of inorganic additives, the line emission of additives can be used as `fingerprints' of the plastics. In this way identification accuracies of 87% to 100% for PE, PP, PET and PVC are achieved.