We present an exhaustive analysis of scalar, electromagnetic, and gravitational perturbations in the background of Schwarzchild-de Sitter and Reissner-Nordstrom-de Sitter spacetimes. The field propagation is considered by means of a semianalytical (WKB) approach and two numerical schemes: the characteristic and general initial value integrations. The results are compared near the extreme cosmological constant regime, where analytical results are presented. A unifying picture is established for the dynamics of different spin fields.6910