A geared positive-displacement machine (10), comprising a housing (11) provided with a suction port and with a discharge port, a pair of gearwheels (14, 15) that are housed and supported by respective shafts (16, 18) for the rotation in a space inside the housing (11) and in fluid communication with the suction port and the discharge port, wherein the gearwheels (14, 15) mesh with each other and have parallel or coinciding axes and a first wheel (14) thereof is driving and a second wheel (15) is driven, a pair of containment bodies (19, 20) for axially containing the wheels (14, 15), said containment bodies (19, 20) being associated with the housing (11) and each comprise a first face (19a, 20a) that faces the pair of gearwheels (14, 15) and a second face (19b, 20b) that is axially opposite with respect to the first face (19a, 20a), and, for each of the two wheels (14, 15), a plurality of rolling bodies (21) that form a crown and that are freely housed in an annular seat (22) that is coaxial to the respective shaft (16, 18) and that is defined at the interface between the first face (19a, 20a) of at least one of the two containment bodies (19, 20) and the surface (14a, 15a; 14b, 15b) of the wheels (14, 15) that in turn faces it, respectively in the first face (19a, 20a) of at least one of the two containment bodies or in the surface (14a, 15a; 14b, 15b) of the gearwheels facing the first face (19a, 20a), wherein the rolling bodies (21) rest on rolling tracks (23, 24) respectively integral with the wheels (14, 15) and with the at least one containment body (19, 20). Between the first face (19a, 20a) of the at least one containment body (19, 20) and the surface (14a, 15a; 14b, 15b) of the wheels (14, 15) facing the first face a distance (D) greater than zero exists.