Energy-energy-correlations (EEC) have been measured with the JADE detector at c.m. energies of 14 GeV, 22 GeV and in the region 29 GeV<E cm<36 GeV. Corrected results are presented of EEC and their asymmetry, which can be directly compared to theoretical predictions. At 〈E cm〉=34 GeV a comparison with second order QCD predictions yields good agreement for the string model fragmentation resulting in a value of the strong coupling constant α s =0.165±0.01 (stat.). The independent fragmentation models, which yield values of α s between 0.10 and 0.15 depending on the treatment of energy and momentum conservation and of the gluon splitting, do not provide a satisfactory description of the data over the full angular range.