Method for the design of rotor and/or stator profiles of a bivalent axial turbomachinery, capable of operating alternatively in driving or operating mode, said turbomachinery comprising at least one stator and one rotor rotatable about a rotation axis, said rotor and/or said stator comprising a hub (16, 15), an ogive and a plurality of blades (14, 13, 155) having substantially the same shape, each of the said blades having a minimum radius, a maximum radius and a three-dimensional blade profile having one or more blade sections (1551, 1552, 1553), where said blade sections (1551, 1552, 1553) are in the shape of two-dimensional aerodynamic profiles each comprising: - a concave side or intrados; - a convex side or extrados; - a median segment as a set of points corresponding to the centers of all the circumferences inscribed in said two-dimensional aerodynamic profile and tangent to the intrados and extrados lines; - a front edge and a rear edge as the locus of geometric points corresponding respectively to the anterior and posterior ends of the median segment; - a half-thickness as the distance between said median segment and said intrados or said extrados, evaluated along the normal to said median segment for each point of said median segment; - a chord or chord segment, as the segment joining the ends of said median segment; - a deflection or camber, that is a function representing the distance that is formed between the said chord and the said median segment when they do not coincide at the points outside the respective ends; said two-dimensional aerodynamic profile being described in a map reference plane (X, Y) by points representing the median segment between the concave side or intrados and the convex side or extrados of the said profile, the chord of the said profile being superimposed on the abscissa in said map reference plane and the origin of the axes of said map reference plane coinciding with the end of the chord next to said front edge, whereby the method comprises - selecting the maximum positive deflection value; - placing the maximum deflection point between 40% and 60% of the chord abscissa; - selecting the ordinate of the median segment with derivative greater than or equal to zero up to the point of maximum deflection and less than or equal to zero after the point of maximum deflection; - placing the point of maximum half thickness between 40% and 60% of the abscissa of the chord; - selecting the radius of the front edge and the rear edge with values greater than or equal to 3% of the length of the chord segment. - a concave side or intrados; - a convex side or extrados; - a median segment as a set of points corresponding to the centers of all the circumferences inscribed in said two-dimensional aerodynamic profile and tangent to the intrados and extrados lines; - a front edge and a rear edge as the locus of geometric points corresponding respectively to the anterior and posterior ends of the median segment; - a half-thickness as the distance between said median segment and said intrados or said extrados, evaluated along the normal to said median segment for each point of said median segment; - a chord or chord segment, as the segment joining the ends of said median segment; - a deflection or camber, that is a function representing the distance that is formed between the said chord and the said median segment when they do not coincide at the points outside the respective ends; said two-dimensional aerodynamic profile being described in a map reference plane (X, Y) by points representing the median segment between the concave side or intrados and the convex side or extrados of the said profile, the chord of the said profile being superimposed on the abscissa in said map reference plane and the origin of the axes of said map reference plane coinciding with the end of the chord next to said front edge, whereby the method comprises - selecting the maximum positive deflection value; - placing the maximum deflection point between 40% and 60% of the chord abscissa; - selecting the ordinate of the median segment with derivative greater than or equal to zero up to the point of maximum deflection and less than or equal to zero after the point of maximum deflection; - placing the point of maximum half thickness between 40% and 60% of the abscissa of the chord; - selecting the radius of the front edge and the rear edge with values greater than or equal to 3% of the length of the chord segment.