Nonsingular models with a variable cosmological term

The weight of observational evidence is now converging on a nonzero Value for the cosmological term Lambda. At the same time, theorists are increasingly exploring the possibility that this parameter is a dynamical one whose effective value in-the early universe may have been quite different from the one we measure today. We discuss two phenomenological Lambda-decay scenarios that have appeared in the literature, focusing on the evolution of the cosmological scale factor. In both cases, observational data are compatible with nonsingular as well as big bang models. Requiring that the "big bounce" be deep enough to generate phenomena such as the cosmic microwave background and primordial light-element abundances, one can predict the present value of Omega(Lambda) if the matter density Omega(o) is known. The acceptable windows are small and overlap the latest observations in several cases of interest.