A cap for closing and opening a container of liquids, in particular beverages, defining a longitudinal axis, comprising: - a supporting element, adapted to be fixed to the container, having a first base portion, coaxial to the longitudinal axis, with a fixing device adapted to engage an aperture of the container; a first intermediate portion, coaxial to the longitudinal axis, on the inner part of which there is a plurality of first grooves inclined by a first angle (α) with respect to a base plane orthogonal to the longitudinal axis; a first vertex portion, coaxial to the longitudinal axis; a first annular sealing surface, coaxial to the longitudinal axis; - a pivotal element, inserted in the supporting element and configured to pivot by a predetermined arc of a circle smaller than 180°, having a second base portion, coaxial to the longitudinal axis; a second intermediate portion, coaxial to the longitudinal axis; a second vertex portion coaxial to the longitudinal axis; a second annular sealing surface, of shape complementary to that of the first annular sealing surface, arranged at the joint between the second base portion and the second intermediate portion, configured to form contact with said first annular sealing surface so as to open and close the container in fluid-tight manner during the use of the cap, characterized in that the first annular sealing surface is arranged at the junction between the first intermediate portion and the first vertex portion; on the outer wall of the second base portion first passages for the passage of liquid and a plurality of guiding teeth inclined by the first angle (α) are formed, which form a first helical kinematic pair with the plurality of first grooves; on the outer wall of the second intermediate portion second passages for the passage of liquid are formed. - a supporting element, adapted to be fixed to the container, having a first base portion, coaxial to the longitudinal axis, with a fixing device adapted to engage an aperture of the container; a first intermediate portion, coaxial to the longitudinal axis, on the inner part of which there is a plurality of first grooves inclined by a first angle (α) with respect to a base plane orthogonal to the longitudinal axis; a first vertex portion, coaxial to the longitudinal axis; a first annular sealing surface, coaxial to the longitudinal axis; - a pivotal element, inserted in the supporting element and configured to pivot by a predetermined arc of a circle smaller than 180°, having a second base portion, coaxial to the longitudinal axis; a second intermediate portion, coaxial to the longitudinal axis; a second vertex portion coaxial to the longitudinal axis; a second annular sealing surface, of shape complementary to that of the first annular sealing surface, arranged at the joint between the second base portion and the second intermediate portion, configured to form contact with said first annular sealing surface so as to open and close the container in fluid-tight manner during the use of the cap, characterized in that the first annular sealing surface is arranged at the junction between the first intermediate portion and the first vertex portion; on the outer wall of the second base portion first passages for the passage of liquid and a plurality of guiding teeth inclined by the first angle (α) are formed, which form a first helical kinematic pair with the plurality of first grooves; on the outer wall of the second intermediate portion second passages for the passage of liquid are formed.