A levelling spacer device for laying slab products (P) for cladding laying surfaces, which comprises: - a support (S) comprising a base (S1), positionable on the backside of a laying surface of at least two slab products (P) that are adjacent and flanked with respect to a flanking direction, and at least one separator element (S2) projecting from said base (S1) and configured and arranged to contact at least a portion of facing flanks of the at least two slab products (P) when said base (S1) is positioned on the backside of said laying surface of the at least two slab products (P), said at least one separator element (S2) being provided with a through-window (So) with an upper edge destined to be located superiorly of the level of an in-view surface of the slab products (P) and a lower edge (L) destined to be located inferiorly of the level of said in-view surface of the slab products (P); and - a presser wedge (W) configured and arranged to be inserted in the through-window (So) and to slide restingly on the in-view surface of the at least two slab products (P), with an upper face (F1) cooperating with the upper edge of the through-window (So) to push the at least two slab products (P) towards the base (S1) of the support (S); wherein said upper face (F1) of the presser wedge (W) comprises at least two adjacent areas (A1, A2) running longitudinally along at least a portion of the length of the pressing wedge (W), characterised in that said areas (A1/A2) are tilted downwards towards each other along a common convergent axis, and in that said upper edge comprises at least two upper tilted sub-edges (U1, U2), each configured and arranged to cooperate with a respective area of the at least two adjacent areas (A1, A2). - a support (S) comprising a base (S1), positionable on the backside of a laying surface of at least two slab products (P) that are adjacent and flanked with respect to a flanking direction, and at least one separator element (S2) projecting from said base (S1) and configured and arranged to contact at least a portion of facing flanks of the at least two slab products (P) when said base (S1) is positioned on the backside of said laying surface of the at least two slab products (P), said at least one separator element (S2) being provided with a through-window (So) with an upper edge destined to be located superiorly of the level of an in-view surface of the slab products (P) and a lower edge (L) destined to be located inferiorly of the level of said in-view surface of the slab products (P); and - a presser wedge (W) configured and arranged to be inserted in the through-window (So) and to slide restingly on the in-view surface of the at least two slab products (P), with an upper face (F1) cooperating with the upper edge of the through-window (So) to push the at least two slab products (P) towards the base (S1) of the support (S); wherein said upper face (F1) of the presser wedge (W) comprises at least two adjacent areas (A1, A2) running longitudinally along at least a portion of the length of the pressing wedge (W), characterised in that said areas (A1/A2) are tilted downwards towards each other along a common convergent axis, and in that said upper edge comprises at least two upper tilted sub-edges (U1, U2), each configured and arranged to cooperate with a respective area of the at least two adjacent areas (A1, A2). <EOS>