We investigate how the country’s absorptive capacity and relative backwardness affect the impact of international R&D spillovers on domestic Total Factor Productivity (TFP). To account for nonlinearities, we adopt a Panel Smooth Transition Regression (PSTR) approach, where the country’s elasticity of TFP to foreign R&D stock is allowed to change smoothly across various identified extreme values, and this change is related to observable transition variables: human capital (capturing the country’s absorptive capacity) and relative backwardness. The results suggest that absorptive capacity is positively associated with international R&D spillovers. In addition, and in contrast with previous results, relative backwardness has a negative and significant impact on them.