they prove' that "the fastest oscillation possible for a solution of (1.4) is at least as fast as the fastest oscillation permitted by equation (1.3)". However, when this result is expressed in terms of zeros of solutions we no longer get the simple separation property characteristic of the second order case. This is not surprising since there always exist nontrivial solutions of (1.3) which vanish at three given points. Thus we must be content with more complicated statements of which the following is typical [1]. THEOREM 1.1. Let u(x) and v(x) be solutions of (1.3) and (1.4), respectively, where the coefficients of the two equations are related by (1.5). If u(x1) = v(x1) = U(X2) = V(X2) = 0 (X1 < X2), and the number of zeros of u(x) and v(x) in [X1 X X2] is denoted by n and m (n _ 4), respectively, then m ? n 1. In this paper the comparison theorems for (1.3) and (1.4) will not be stated in terms of separation of zeros. Instead we shall consider a slightly more general form of comparison theorem which permits a direct generalization to the fourth order case. In the second order case the appropriate generalization of Sturm's theorem is well known and can also be obtained by the method of ?3. It deals with functions u(x) and v(x) which are, respectively, solutions of (1.1) and (1.2) where q(x)