Abstract.Let k be any imaginary abelian field with conductor not exceeding 100, where an abelian field means a finite abelian extension over the rational field Q contained in the complex field. Let C(k) denote the ideal class group of k , C~(k) the kernel of the norm map from C(k) to the ideal class group of the maximal real subfield of k , and f(k) the conductor of k ; f(k) < 100 .Proving a preliminary result on 2-ranks of ideal class groups of certain imaginary abelian fields, this paper determines the structure of the abelian group C~~(k) and, under the condition that either [k : Q] < 23 or f(k) is not a prime > 71 , determines the structure of C(k).We shall mean by an abelian field a finite abelian extension over the rational