Abstract. By L(G) we denote a line graph of G. We set L⁰(G)=G. For i>0 the i-iterated line graph of G is Lⁱ(G)=L(L^i-1(G)).

We prove that if G is a connected graph with the minimum degree d>2, then the connectivity of L²(G) is at least d-1. However, if G is 4-connected, then the connectivity of L²(G) is at least 4d-6.

This later result, combined with a result of Hartke and Higgins about the growth of minimum degree in iterated line graphs (published later), implies that for every graph G there is a number i_G such that the connectivity of Lⁱ(G) equals the minimum degree of Lⁱ(G) when i>=i_G. For regular graphs we do not need the statement of Hartke and Higgins, and in this case i_G<=5.