This thesis is an extension and generalization of the works done by Kaslik and Balint, and Shu and Wei . Since in most cases and specially in applications, the internal decay of the neurons are different, therefore in this thesis we have extended and generalized the Hopfield neural network with ring structure with equal internal decays to a neural network with different internal decays. We also have generalized and extended the bidirectional associative memory (BAM) with three neurons to a system with p+1 neurons. A bifurcation analysis is undertaken for these discrete-time neural networks with multiple delays. The stability domains of the null solution for each system is found, the critical values of the characteristic parameters for which the characteristic equation has root or roots on the unit circle and bifurcations occur at the origin are identified. In several lemmas, we investigated properties of these critical values and necessary conditions to occur bifurcation for them. Then, according to type of eigenvalue or eigenvalues which are on the unit circle the existence of Fold/Cusp, Neimark-Sacker and Flip bifurcations are proved. Their stability and bifurcation direction are analyzed by applying the center manifold theorem and the normal form theory. In addition about Neimark-Sacker bifurcation, it is proved that resonant 1:3 and 1:4 bifurcations may also be present, therefore necessary condition for this type of bifurcation is explained. In Hopfield network, it is shown that the dynamics of network in a neighborhood of the null solution become more and more complex as the characteristic parameter grows in magnitude and passes through the bifurcation values. A theoretical proof is given for the occurrence of Marotto's chaotic behavior in these neural networks, if the magnitudes of the interconnection coefficients are large enough and at least one of the activation functions has two simple real roots. But the story is different about the bidirectional associative memory and as the characteristic parameter grows in magnitude the chaos phenomena doesn't occur in system, because it is not possible to find a snap-back repeller point for this neural network. At the end of each section, some graphs and numerical simulations consisting of bifurcation diagram, phase portrait and Lyapunov exponents are presented for variety values of bifurcatio parameters.