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• EU countries are classified in four groups based on energy efficiency trajectories. • Domestic energy systems co-evolve with innovation system and policy mix. • Structural change and export competitiveness are affected by the systems co-evolution. • Positive spillovers arise between countries with similar policy mix and high trade relations. • International knowledge and policy spillovers lead to high innovative and competitiveness performances. This paper aims to analyse the evolution of energy efficiency systems for the residential sector of EU countries over the past twenty years and the associated process of structural change occurred in EU economies. To this purpose, we develop a set of indicators to measure some significant characteristics of the energy efficiency systems focusing on the residential sector and map European countries in terms of four dimensions: energy system, innovation pattern, policy mix design and export competitiveness. Building on these indicators we develop a cluster analysis identifying non-arbitrary homogeneous country groups according to several characteristics in order to investigate the co-evolution of technological trajectories, energy use performance and export competitiveness in this specific domain. Results suggest the distinction of EU countries into four groups, that are individually and comparatively scrutinized shedding light on how the four dimensions here considered dynamically evolved and interacted within and across countries. Empirical findings suggest that the design of the domestic policy mix may influence technological trajectories and structural change processes. Such effect appears to be related to the quality and dimension of international relationships with main economic partners. [ABSTRACT FROM AUTHOR]