With the use of a mean-square difference criterion to distinguish echoes from two targets at different ranges moving with different velocities, an ambiguity function is derived. The concept of a modulated carrier is avoided, and the actual Doppler effect of time compression or expansion is used, rather than the more usual approximation of constant frequency shift. Thus this function can be applied to the very-low-frequency broadband signals sometimes employed in sonar systems. It reduces to the Woodward ambiguity function in the case of two targets of nearly equal velocity, and, in general, in a narrow-band approximation. Some properties of this ambiguity function are discussed.