  Motivated by data on the evolution of the Internet and World Wide Web we
consider scenarios of self-organization of the nonlinearly growing networks
into free-scale structures. We find that the accelerating growth of the
networks establishes their structure. For the growing networks with
preferential linking and increasing density of links, two scenarios are
possible. In one of them, the value of the exponent $\gamma$ of the
connectivity distribution is between 3/2 and 2. In the other, $\gamma>2$ and
the distribution is necessarily non-stationary.
