Denote by V_f~p the set of homotopy classes of codimensiom m framings of the p thorder stable normal bundle of a map f:M~n→N~(v(n,p)+m). Where 3≤m=n-1 or m=n-2 but n=0,1 mod 4. We determine in this paper the set V_f~p and then the set of p-homotopy classes of p-immersions homotopic to f for some special cases.