In this work the performance of neural networks in solving some combinatorial optimization problems was checked. The investigation included quantized, binary and continuous Hopfield networks and some variants of the quantized Hopfield network, namely the fixed-weighted Boltzman machine and the fluctuation technique.A new model for the Hopfield network has been presented in this thesis, which is constructed from the fusion of wo neural networks, namely quantized Hopfield network and the fixed-weighted Boltzman machine. The new model gives good results with less computer time. Specifically, the assignment problems and transportation problems are solved, using the computer programs written in turbo Pascal and Visual Basic 6.0, running on Pentium II personal computer. The results were in agreement with the results of well-established linear programming algorithms, as well as less computer time.