Every group G has a unique maximal normal locally nilpotent subgroup $Phi(G)$, called the Hirsh-Plotkin radical of G [9]. If G is a group, we define the upper Hirsh-Plotkin series of G to be the ascending series $1 = R_0 leq R_1 leq ldots$ in which $R_{alpha+1}/R_alpha = {Phi(G/R_alpha)$ for each ordinal $alpha and R_eta = cup_{alpha<eta}R_alpha$ for each limit ordinal $eta$. If $R_r = G$ for some natural number r, then G is said to have locally nilpotent length r. $(LN)^r$ denotes the calss of groups of locally nilpotent length at most r.