We present a study of forces between highly charged macroscopic mica surfaces in the presence of dilute aqueous solutions of ethylenediamine (divalent) and spermidine (trivalent). In the concentration range 10(-5)-10(-4) M diamine, the electrostatic double-layer repulsion diminishes progressively; it disappears altogether with 10(-3) M diamine, leaving a strong attraction. In contrast, at equivalent concentrations of spermidine, the force is first attractive and then exhibits a repulsive region as the concentration is increased. This indicates a reversal of double-layer charge. The surfaces can only be made to approach to within 8 and 12 Angstrom of each other respectively for diamine and spermidine, which suggests the strong participation of these counterions in neutralizing the surface charge. The strengths of attractions have been measured as a function of separation and are seen to exceed the van der Waals forces anticipated between mica surfaces across water. The attraction, the double-layer charge inversion, and the significant diminution of electrostatic repulsion are argued to be consequences of ion-correlation effects.