The offshoring of high-tech services has greatly increased in recent years, with consequences for firms demand for skilled employment in firms. This paper specifically analyzes the relationship between R&D offshoring and the demand for R&D employment using firm-level data for Spanish manufacturing and services companies during the period 2004-2009. Estimating different specifications with panel data techniques, we find that this association is statistically positive. In particular for services firms a 1 percentage point increase in R&D offshoring raises the demand for researchers by about 11%. This suggests the existence of complementarity among them as productive inputs.