Let \(H\) be a graph. Then a graph \(G\) is said to be locally \(H\) if for any vertex \(v\) of \(G\) the subgraph of \(G\) induced by neighbours of \(v\) is isomorphic to \(H\). In the paper, an upper bound on the diameter of a locally \(H\) graph is given for many graphs \(H\) of diameter 2.