A machine for packaging articles, in particular CDs, DVDs and the like, into relative containers, which are formed by a pair of substantially box-like closure members, lower (GD and upper (G2), hinged to each other along a common hinge edge (D), includes a conveying line (L), which is equipped all around with gripping and transferring devices (1). The gripping and transferring devices (1) are moved continuously and grip lateral edges of die iowa closure member (G1) of the containers (C) housed in closed condition inside a magazie (S0) and remove the containers (C) from the bottom of the magazine (S0). The gripping and transferring devices (1) transfer the containers withdrawn from the magazine (S0) to subseqaent working stations associated to the line (L). The working stations, in suitable and mutual time relation with the forward movement of the gripping and transferring devices (1), open the containers by opening the upper closure member (G2) with respect to the lower closure member (G1), insert at least one informative leaflet (Li) and at least one of said articles (10) into the closure members, insert a cover sheet F between the closure members (G1, G2) and a protective film applied onto the closure members, and finally, close the container