Couples looking for jobs in the same labor market may cause instabilities. We determine a natural preference domain, the domain of weakly responsive preferences, that guarantees stability. Under a restricted unemployment aversion condition we show that this domain is maximal for the existence of stable matchings. We illustrate how small deviations from (weak) responsiveness, that model the wish of couples to be closer together, cause instability, even when we use a weaker stability notion that excludes myopic blocking. Our remaining results deal with various properties of the set of stable matchings for >responsive couples markets>, viz., optimality, filled positions, and manipulation. © 2004 Elsevier Inc. All rights reserved.

B. Klaus’s and F. Klijn’s research is supported by Ramón y Cajal contracts of the Spanish Ministerio de Ciencia y Tecnología. The main part of F. Klijn’s work was supported by a Marie Curie Fellowship of the European Community programme ‘‘Improving Human Research Potential and the Socio-economic Knowledge Base’’ under contract number HPMF-CT-2001-01232, carried out at the Departament d’Economia i d’Història Econòmica, Universitat Auònoma de Barcelona. The work of the authors is partially supported by Research Grant BEC2002-02130 from the Spanish Ministerio de Ciencia y Tecnología and by the Barcelona Economics Program of CREA.

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