A mechanism for closing and opening a swinging-sliding door leaf, which is shifted to open it in a first outward swinging movement and in a second parallel sliding movement outside the wall in which the door frame is located, comprising - fixed to the upper door frame, a horizontal support guide over which a carriage slides in a rectilinear and alternating back and forth movement for closing and opening the door; a groove-cam which is almost entirely rectilinear, except in at least one of its ends in which it forms a curvilinear portion towards one of the sides of the door; and means for the slidable suspension of the leaf, attached in an articulated manner to the mentioned frame; and - fixed to the door leaf, a vertical-axis wheel suitable for travelling inside the groove-cam during the opening and closing movements of the leaf, wherein the means for the slidable suspension of the leaf comprise a horizontal bar pivotably suspended at its ends from the upper door frame, in which a sleeve integral with the leaf is slidably assembled, and the mechanism further comprises a push-pull connecting rod, fixed in an articulated manner at its ends to the carriage and to the upper part of the door leaf such that, during the shifting of the leaf from its open position to its closed position, the connecting rod adopts an essentially longitudinal position parallel to the path of the door in which, in the forward movement direction of the carriage, its first point of articulation with the door leaf remains in front of the imaginary line transverse to the guide passing through its second point of articulation with the carriage; whereas when the carriage reaches the end of its path on the horizontal guide, when the wheel travels over said curvilinear portion, the connecting rod is forced to rotate about the second point of articulation until its first point of articulation is located slightly behind the mentioned imaginary line, whereby the connecting rod is locked against possible openings by pushing the door leaf in its opening direction. - fixed to the upper door frame, a horizontal support guide over which a carriage slides in a rectilinear and alternating back and forth movement for closing and opening the door; a groove-cam which is almost entirely rectilinear, except in at least one of its ends in which it forms a curvilinear portion towards one of the sides of the door; and means for the slidable suspension of the leaf, attached in an articulated manner to the mentioned frame; and - fixed to the door leaf, a vertical-axis wheel suitable for travelling inside the groove-cam during the opening and closing movements of the leaf, wherein the means for the slidable suspension of the leaf comprise a horizontal bar pivotably suspended at its ends from the upper door frame, in which a sleeve integral with the leaf is slidably assembled, and the mechanism further comprises a push-pull connecting rod, fixed in an articulated manner at its ends to the carriage and to the upper part of the door leaf such that, during the shifting of the leaf from its open position to its closed position, the connecting rod adopts an essentially longitudinal position parallel to the path of the door in which, in the forward movement direction of the carriage, its first point of articulation with the door leaf remains in front of the imaginary line transverse to the guide passing through its second point of articulation with the carriage; whereas when the carriage reaches the end of its path on the horizontal guide, when the wheel travels over said curvilinear portion, the connecting rod is forced to rotate about the second point of articulation until its first point of articulation is located slightly behind the mentioned imaginary line, whereby the connecting rod is locked against possible openings by pushing the door leaf in its opening direction.