A machine for making absorbent sanitary articles includes a feed conveyor on which a continuous web of material for making the articles is advanced along a feed line in a first direction. A forming and application unit forms and applies by which at least one pair of accessory elements for each article and includes a device for feeding a continuous succession of accessory elements and a conveying unit. The conveying unit includes a conveyor roller for the continuous succession of accessory elements, and a separating device defined by a first and a second spacer roller which are substantially tangent to the conveyor roller at a first and a second pickup station, respectively. The first and the second spacer roller have retaining and alternate movement devices including respective pickup pads which are slidable along a second direction and which are driven by a respective linear electric motor.