A machine for the dyeing of reels of yarn and/or of textile fibre wound on packages, comprising: a structure delimiting at least one chamber at least partially or completely filled with at least one dyeing fluid, in which a dye has been dispersed; support means placed within said chamber, in a position that is at least partially immersed in said dyeing fluid, said support means comprising at least one hollow support plate having a plurality of hollow support parts, each of which is equipped with a series of hollow reel-holder rods; recirculation means operationally associated with at least one reel-holder rod to induce said dyeing fluid to pass through said reel-holder and the respective reel and/or textile fibre wound on a package that is slotted onto said reel-holder, on an intermittent basis, said recirculation means comprising: an initial recirculation mechanism operationally interposed between said chamber and said support plate to induce said dyeing fluid to flow between at least one of said reel-holder rods and said chamber; at least one selection mechanism operationally interposed between said initial recirculation mechanism and a corresponding hollow support part, each selection mechanism being able to switch between an open position, in which said initial recirculation mechanism induces said dyeing fluid to pass through at least one reel-holder of the respective hollow support part, and a closed position, in which said dyeing fluid does not pass through said reel-holder rod of the respective hollow support part; at least one second recirculation mechanism operationally associated with said structure to induce sufficient transit of the dyeing fluid within said chamber on at least one set closed and/or loop routes, sufficient to maintain uniform concentrations of dye and dyeing fluid temperature. a structure delimiting at least one chamber at least partially or completely filled with at least one dyeing fluid, in which a dye has been dispersed; support means placed within said chamber, in a position that is at least partially immersed in said dyeing fluid, said support means comprising at least one hollow support plate having a plurality of hollow support parts, each of which is equipped with a series of hollow reel-holder rods; recirculation means operationally associated with at least one reel-holder rod to induce said dyeing fluid to pass through said reel-holder and the respective reel and/or textile fibre wound on a package that is slotted onto said reel-holder, on an intermittent basis, said recirculation means comprising: an initial recirculation mechanism operationally interposed between said chamber and said support plate to induce said dyeing fluid to flow between at least one of said reel-holder rods and said chamber; at least one selection mechanism operationally interposed between said initial recirculation mechanism and a corresponding hollow support part, each selection mechanism being able to switch between an open position, in which said initial recirculation mechanism induces said dyeing fluid to pass through at least one reel-holder of the respective hollow support part, and a closed position, in which said dyeing fluid does not pass through said reel-holder rod of the respective hollow support part; at least one second recirculation mechanism operationally associated with said structure to induce sufficient transit of the dyeing fluid within said chamber on at least one set closed and/or loop routes, sufficient to maintain uniform concentrations of dye and dyeing fluid temperature. an initial recirculation mechanism operationally interposed between said chamber and said support plate to induce said dyeing fluid to flow between at least one of said reel-holder rods and said chamber; at least one selection mechanism operationally interposed between said initial recirculation mechanism and a corresponding hollow support part, each selection mechanism being able to switch between an open position, in which said initial recirculation mechanism induces said dyeing fluid to pass through at least one reel-holder of the respective hollow support part, and a closed position, in which said dyeing fluid does not pass through said reel-holder rod of the respective hollow support part; at least one second recirculation mechanism operationally associated with said structure to induce sufficient transit of the dyeing fluid within said chamber on at least one set closed and/or loop routes, sufficient to maintain uniform concentrations of dye and dyeing fluid temperature.