Assembly comprising at least two covering strips (1; 1'; 1"; 1"'), each covering strip comprising a substantially planar rear face, and at least two opposite edges (12, 13) provided with complementary coupling elements respectively comprising a groove and a tongue which can be engaged in the groove, said groove being delimited by two front and rear lips, said coupling elements making it possible to couple edge-to-edge, with or without play, the two covering strips with their rear faces substantially coplanar, such that, once the two strips have been coupled with one another, there is at least one contact or quasi-contact region (Z 1) between the tongue and the inner face of the rear lip, the coupling elements additionally comprising mechanical locking means (123, 133) which prevent, with or without play, the reciprocal moving apart of two coupled strips, in a plane (X, Z) parallel to their lower face and in a direction perpendicular to their coupled edges, said assembly additionally comprising laying accessories allowing the strips to be secured to a wall, and in particular to a non-horizontal wall or to a ceiling so as to form a strip coating, each laying accessory comprising at least one connection element (2; 2'; 2"; 2"'; 2""; 2""'), which comprises a first part adapted to be positioned in the groove of a strip, and in contact with the inner face of the rear lip at least in a region at least partially covering said contact or quasi-contact region (Z 1) between the rear lip and the tongue in the absence of a connection element, and a second part which makes it possible to secure the connection element (2; 2'; 2"; 2"'; 2""; 2""') to a wall, characterized in that at least one of the two lips is deformable and/or in which at least one of the two lips is compressible, and/or in which the first part of the connection element can be squashed, in which the thickness (e 1) of said first part of the connection element is greater than the distance separating the inner face of the rear lip and the tongue in said contact or quasi-contact region (Z 1) in the absence of a connection element, but is sufficiently small such that, once said first part of the connection element is positioned in the corresponding groove of a strip, by virtue, where appropriate, of said elasticity of at least one of the two lips and/or by virtue of the squashing of the first part of the connection element, the two strips can still be coupled with one another, with a clamping of the first part of the connection element between the rear lip and the tongue introduced into the groove, at least in a region corresponding to said contact or quasi-contact region (Z 1) between the tongue and the rear lip of the groove in the absence of a connection element, and in that the inner face of the rear lip has a non-rectilinear profile, and the first part of a connection element (2; 2'; 2"; 2"') is formed so as to hug said non-rectilinear profile once said first part of a connection element (2; 2'; 2"; 2"') is positioned in the groove, or in that the inner face of the rear lip has a non-rectilinear profile, and the first part of a connection element (2""; 2""') is deformable so as to hug said non-rectilinear profile once said first part of a connection element is positioned in the groove.