In this note we study the National Resident Matching Program (NRMP) algorithm in the US market for physicians. We report on two problems that concern the presence of couples, a feature explicitly incorporated in the new NRMP algorithm (cf. Roth and Peranson in Am Econ Rev 89:748–780, 1999). First, we show that the new NRMP algorithm may not find an existing stable matching, even when couples’ preferences are ‘responsive’, i.e., when Gale and Shapley’s (Am Math Monthly 69:9–15, 1962) deferred acceptance algorithm (on which the old NRMP algorithm is based) is applicable. Second, we demonstrate that the new NRMP algorithm may also be anipulated by couples acting as singles.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 Autònoma 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.