Wear mechanisms of three Ag-Cu eutectic alloy samples cooled at different rates from the melt have been investigated by friction force microscopy. The eutectic phase exhibits a lamellar structure where the interlamellar thickness decreases with increasing cooling rate. The hardness of the samples decreases with decreasing thickness of the lamellae. In the low normal force regime (F(n)1000nN) friction is governed by shearing and the relevant contact area can be well described by the Johnson-Kendal-Roberts model. At higher normal force values, the surface is worn, and friction can be described by the ploughing friction coefficient. A ploughing friction coefficient is determined, which is positively correlated with the hardness of the Ag-Cu eutectic alloy samples cooled at different rates, while the wear volume negatively correlates with the hardness.