An apparatus for detwisting wires or cables wound in spools, includes two coaxial shafts, inserted one inside another and kinematically independent, of which a first shaft is connected to a first motor and is adapted to support, by rotating it about a rotation axis, one spool, and a second shaft is connected to second motor and supports, by rotating it about the rotation axis, a detwisting cage, which is adapted to rotate about the spool. The apparatus further includes at least one take up guide for the wire/cable, which is connected to a third motor in order to rotate about the rotation axis of the cage, oscillating toward the guide and/or away from it, and elements for coordination of the rotation speed of the first shaft with the rotation speed of the take up guide.