Described is a machine for making absorbent sanitary articles, according to this invention, comprising a device (10) for feeding a continuous strip (9) to a conveyor roller (1 1 ) and to a device (12) for cutting the strip (9) into a continuous and alternating succession (13) of first (14) and second (15) pieces, a unit (20) for forming and applying on a continuous band (22) of absorbent material at least a pair of first (14) and second (15) pieces, aligned and spaced by a distance (d), for each absorbent article (2) a device (23) for cutting the continuous band (22) into pieces (24) of absorbent material designed to constitute single absorbent articles (2) a first (16) and a second (17) roller each comprising a plurality of units (18,19) for the picking up and the successive release of the first (14) and the second (15) pieces, and a plurality of concentric units (28a, 28b, 28c) rotating, independently of each other, about a shared axis (B, C) of rotation, each of which carrying at least one unit (18, 19) motor means (30) for defining a respective law of motion for each of the units (28a, 28b, 28c) and means (39) for translating the units (18, 19), between a position for picking up the pieces (14, 15), at the conveyor roller (1 1 ), and a position for releasing the pieces (14, 15), at the forming and applying unit (20).Une machine de fabrication darticles hygiéniques absorbants, selon la présente invention, comprend un dispositif (10) pour acheminer une bande continue (9) à un rouleau transporteur (11) et un dispositif (12) pour couper la bande (9) en une succession continue et alternée (13) de premier (14) et second (15) morceaux, une unité (20) pour former et appliquer, sur une bande continue (22) de matériau absorbant, au moins une paire de premier (14) et second (15) morceaux, alignés et espacés dune distance (d), pour chaque article absorbant (2) un dispositif (23) pour couper la bande continue (22) en morceaux (24) de matériau absorbant conçus pour constitue