Complexity, heterogeneity, interdependencies and, especially, evolution of system/services specifications, related operating environments and user needs, are more and more highly relevant characteristics of modern and future software applications. Taking advantage of the experience gained in the context of the European project CONNECT, which addresses the challenging and ambitious topic of eternally functioning distributed and heterogeneous systems, in this paper we present a framework to analyse and assess dependability and performance properties in dynamic and evolving contexts. The goal is to develop an adaptive approach by coupling stochastic model-based analysis, performed at design time to support the definition and implementation of software products complying with their stated dependability and performance requirements, with run-time monitoring to re-calibrate and enhance the dependability and performance prediction along evolution. The proposed framework for adaptive assessment is described and illustrated through a case study. To simplify the description while making more concrete the approach under study, we adopted the setting and terminology of the CONNECT project.