Convergence time in Hopfield attractor neural network with parallel dynamics is investigated by computer simulation of networks of extremely large size (up to the number of neurons N=10/sup 5/). A special algorithm is used to avoid storage in the computer memory of both connection matrix and the set of stored prototypes. Thus, the size of the simulated network is restricted only by the processing time. It is shown that asymptotically for N/spl rarr//spl infin/ the number of time steps S which are required to reach the attractor in the vicinity of the recalled prototype is proportional to N/sup /spl gamma// where power index /spl gamma//spl Lt/1.