The invention relates to a tongue-and-groove coupling between panels of self-supporting air-conditioning ducts and the like, of the type that is provided in order to establish an optimum fit of the canted edge corresponding to the panels that are coupled in a tongue-and-groove manner, and also, to avoid the air coming into contact with the core of the duct therein. To this end, the panels consist of a core of insulating material complemented by an outer layer and inner layer based on aluminum or some other coating, the juxtaposing canted edge or edge between the panels having an oblique cut in relation to the horizontality or longitudinal intermediate line in the joint between the two panels; the aluminum layer or coating, which determines the inner face of the duct, extending beyond the edge of the panel, and being fixed to the oblique surface that defines the coupling profile.