The group Aut Γ of automorphisms of Rado's universal graph Γ (otherwise known as the ‘random’ graph: see [1]) and the corresponding groups Aut Γc for C a set of ‘colours’ with 2 ≤ |C| ≤ ℵ0, were studied in [4]. It was shown that Aut Γc is a simple group, and the possible cycle types of its members were classified. A natural extension of Aut Γc to a highly transitive permutation group on the same set is obtained by considering the ‘almost automorphisms’ of Γ. It is the purpose of the present paper to answer similar questions about the resulting group AAut Γc. Namely we shall classify its normal subgroups and the cycle types of its members. The main result on normal subgroups is summed up in Corollary 2·9, which says that the non-trivial normal subgroups of AAut Γc form a lattice isomorphic to the lattice of subgroups of the free Abelian group of rank n where n = |C| – 1, and for cycle types it will be shown that those occurring in AAut Γc are precisely the same as in Aut Γc except for those which are the product of finitely many cycles.