The relative demand for skills has increased considerably in many OECD countries during recent decades. This development is potentially explained by capital-skill complementarity and high growth rates of capital equipment. When production functions are characterized by capital-skill complementarity, relative wages and employment of skilled labor are countercyclical because capital equipment is a quasi-fixed factor in the short run. The exact behavior of the two variables depends on relative wage flexibility. Relative wages are rigid in Denmark, implying that the employment share of skills should be countercyclical. The labor market is competitive in the United States and therefore relative wages of skilled labor are expected to be countercyclical. We find that the business cycle development of the two economies is consistent with capital-skill complementarity.