It had been shown previously that the dynamic viscosities measured by superposing in‐line and transverse small‐amplitude oscillations on steady simple shearing were independent of the base rate of shear at ultrasonic frequencies in the BKZ fluid. This result was derived on the assumption that the shear relaxation modulus had a bounded right‐hand derivative at the origin. The present investigation proves this same result without this assumption. A similar conclusion is derived for the derivative of the storage modulus at high frequencies. In addition, it is shown that these ultrasonic measurements cast light on the question of the boundedness of the first two derivatives of the relaxation modulus at the origin.