A machine for performing wire windings on cores arranged on the internal lateral surface of cylindrical stators for electric motors, comprising: - a footing provided with first supporting means adapted to keep a substantially cylindrical stator in a winding position, in which it is arranged so that its axis is aligned with a substantially vertical main axis; - means of moving said stator, which comprise means of rotating the stator about its own axis with respect to said footing; - second means of supporting at least two winding heads above said footing; - means of actuating said at least two winding heads along a first direction that is substantially parallel to said main axis and along a second direction that is substantially perpendicular to said main axis, with respect to said second supporting means; each one of said winding heads being provided with a tip that supports a wire guiding tube that can face, with its end for dispensing the wire to be wound, the internal lateral surface of the stator and which can be oriented substantially at right angles to said main axis; said at least two winding heads being insertable with their tip into said stator and actuatable simultaneously in order to simultaneously perform the winding of at least two cores of the stator which protrude from the internal lateral surface of said stator, each one of said winding heads comprising a head body and a tip that is associated, so that it can rotate about a secondary axis that is substantially perpendicular to said main axis, with said head body and which supports said wire guiding tube; means being provided for moving said tip for its rotation about said secondary axis with respect to said head body, wherein said wire guiding tube can be arranged, by virtue of the action of said movement means of said tip, at least in a first position, in which it is arranged parallel to said main axis, in a second position, in which it is arranged at right angles to said main axis, and in a third position, in which it is arranged parallel to said main axis but is oriented in the opposite direction with respect to said first position. - a footing provided with first supporting means adapted to keep a substantially cylindrical stator in a winding position, in which it is arranged so that its axis is aligned with a substantially vertical main axis; - means of moving said stator, which comprise means of rotating the stator about its own axis with respect to said footing; - second means of supporting at least two winding heads above said footing; - means of actuating said at least two winding heads along a first direction that is substantially parallel to said main axis and along a second direction that is substantially perpendicular to said main axis, with respect to said second supporting means; each one of said winding heads being provided with a tip that supports a wire guiding tube that can face, with its end for dispensing the wire to be wound, the internal lateral surface of the stator and which can be oriented substantially at right angles to said main axis; said at least two winding heads being insertable with their tip into said stator and actuatable simultaneously in order to simultaneously perform the winding of at least two cores of the stator which protrude from the internal lateral surface of said stator, each one of said winding heads comprising a head body and a tip that is associated, so that it can rotate about a secondary axis that is substantially perpendicular to said main axis, with said head body and which supports said wire guiding tube; means being provided for moving said tip for its rotation about said secondary axis with respect to said head body, wherein said wire guiding tube can be arranged, by virtue of the action of said movement means of said tip, at least in a first position, in which it is arranged parallel to said main axis, in a second position, in which it is arranged at right angles to said main axis, and in a third position, in which it is arranged parallel to said main axis but is oriented in the opposite direction with respect to said first position.