  In this paper we calculate the average number of cliques in random scale-free
networks. We consider first the hidden variable ensemble and subsequently the
Molloy Reed ensemble. In both cases we find that cliques, i.e. fully connected
subgraphs, appear also when the average degree is finite. This is in contrast
to what happens in Erd\"os and Renyi graphs in which diverging average degree
is required to observe cliques of size $c>3$. Moreover we show that in random
scale-free networks the clique number, i.e. the size of the largest clique
present in the network diverges with the system size.
