The authors have analyzed the dynamics of associative neural networks based on macroscopic state equations and have shown that both a layered associative net and an autocorrelation type net have the same convergence property: If a recalling process succeeds, the network converges very fast to one of the memorized patterns. But if a recalling process fails, it converges very slowly to a spurious state or does not converge. This property was also checked by computer simulations on a large scale (N = 1000) neural network. Moreover, it is shown that the convergence time for a successful recall is of order log(N). If this convergence time difference is used, execution time and memory can be saved and it can be determined whether a recalling process succeeds or fails without any additional procedure.