2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/178600In the framework of extended gravity theories, we discuss the meaning of a time dependent "cosmological constant" and give a set of conditions to recover asymptotic de Sitter behaviour for a class of cosmological models independently of initial data. To this purpose we introduce a time-dependent (effective) quantity which asymptotically becomes the true cosmological constant. We will deal with scalar-tensor, fourth and higher than fourth-order theories.24 pages, Latex, submitted to Gen.Rel.and GravGeneral Relativity and Quantum Cosmologytext