A machine for producing wire windings on rotor or stator cores, comprising: - a main supporting structure; - a first support, which is associated with said main supporting structure; - a spindle with a horizontal axis, which is supported so that it can rotate about its own axis by said first support and can be actuated with a rotary motion about its own axis; - a second support, which is associated with said main supporting structure; - a tailstock, which is arranged opposite and coaxially with respect to said spindle and is supported so that it can rotate about its own axis by said second support; - a third support, which is supported by said main supporting structure and can move on command along three mutually perpendicular axes (13, 14, 15), respectively along two horizontal axes (13, 14) and along a vertical axis; at least one between said first support and said second support being movable with respect to the other along a direction that is parallel to the axis of said spindle and of said tailstock and said third support being provided with means for detachable engagement with components (62, 64, 81, 102, 136, 137) of equipment for dispensing and/or cutting wires (67, 86, 109, 139) to be wound around rotor or stator cores (53, 72, 93, 122) that can be fitted between said spindle and said tailstock; characterized in that said spindle and said tailstock are configured for being connected to at least one apparatus for wounding rotor or stator cores, wherein, in order to render the machine capable of producing different types of windings, said spindle and said tailstock are adapted to take different types of winding configurations including at least one of the following winding configurations, each configuration being associated to a respective apparatus: a) a configuration in which said rotor or stator cores are arranged mutually side by side parallel to the axis of said spindle and of said tailstock; b) a configuration in which said rotor or stator cores are arranged so that their axes lie on a plane that is perpendicular to the axis of said spindle and of said tailstock and are arranged so as to be radially and angularly mutually spaced around the axis of said spindle and of said tailstock; c) a configuration in which said rotor or stator cores are arranged coaxially to said spindle and to said tailstock. - a main supporting structure; - a first support, which is associated with said main supporting structure; - a spindle with a horizontal axis, which is supported so that it can rotate about its own axis by said first support and can be actuated with a rotary motion about its own axis; - a second support, which is associated with said main supporting structure; - a tailstock, which is arranged opposite and coaxially with respect to said spindle and is supported so that it can rotate about its own axis by said second support; - a third support, which is supported by said main supporting structure and can move on command along three mutually perpendicular axes (13, 14, 15), respectively along two horizontal axes (13, 14) and along a vertical axis; a) a configuration in which said rotor or stator cores are arranged mutually side by side parallel to the axis of said spindle and of said tailstock; b) a configuration in which said rotor or stator cores are arranged so that their axes lie on a plane that is perpendicular to the axis of said spindle and of said tailstock and are arranged so as to be radially and angularly mutually spaced around the axis of said spindle and of said tailstock; c) a configuration in which said rotor or stator cores are arranged coaxially to said spindle and to said tailstock.