  The distribution of motifs in random hierarchical networks defined by
nonsymmetric random block--hierarchical adjacency matrices, is constructed for
the first time. According to the classification of U. Alon et al of network
superfamilies by their motifs distributions, our artificial directed random
hierarchical networks falls into the superfamily of natural networks to which
the class of neuron networks belongs. This is the first example of ``handmade''
networks with the motifs distribution as in a special class of natural networks
of essential biological importance.
