This paper elicits an in-depth discussion on equivalence of current dual-porosity poroelastic (DPP) models in terms of their parametric compatibilities, which are shown to break down when physical implications of each model are further probed. The majority of existing DPP models envision the elastic parameters either as those characterizing the matrix blocks only or as the lumped ones delineating for both the matrix blocks and fractures. The flaw of the former characterization is that it neglects the important impact of fracture deformation which should be substantially larger than the matrix deformation because of its greater compressibility; the drawback of the latter delineation is that it omits the significant difference between the matrix and fracture deformations which cannot offer a clear vision for the relevant experimental studies. As a remedy to these approaches, modifications of the parametric relationships in the existing DPP models are provided to accommodate the compatibility requirements. In addition, as an effort to minimize conceptual conflicts in the associated DPP models, sensible formats of the effective stress laws for the dual-porosity media are presented. The revised effective stress law facilitates the extension of the DPP model to multiporosity poroelastic formulations. ¿ 1999 American Geophysical Union