An expansion anchor assembly for use in a borehole formed in a receiving material has a leading end and a trailing end relative to the insertion direction of the assembly into the borehole. The expansion anchor assembly includes a tie rod with an expansion cone at its leading end, an expansion sleeve through which the tie rod extends and a cone sleeve positioned around the expansion cone and between the expansion cone and the leading end of the expansion sleeve. The radially outer surfaces of the expansion cone and the cone sleeve each have a different cone angle. Due to the different once angle, when the tie rod is drawn into the expansion sleeve toward the trailing end of the assembly, the part with the smaller cone angle moves in the same direction into the expansion sleeve until it contacts a stop. Subsequently on continued inward movement of the tie rod, both the expansion cone and the cone sleeve are drawn into the leading end of the expansion sleeve and effect an increased expanding action.