Abstract: LetX₁,…,X_n be a sequence of p-diniensionali.i.d. random vectors, aud Z₁, …, Z_n be i.i.d. N_p（0,l_p） random vectors in R^p, which are independent of X_i’s. In this paper, we give the rep-resentition of the class of limit distributions of \hatF_n^Z / B_p, \hatF_n^Z_1 / B_p, where \hatF_n^Z / B_p, \hatF_n^Z_1 / B_p stands for emperical distribution of Z^TX_i/B_p, i≤n, Z_i^Tx_i/B_p,i≤n respectively, as n→+∞, p→+∞, and B_p is a sequence of positive numbers.