Grafting carbon nanotubes (CNTs) directly on carbon fibers represents a promising approach in order to strengthen the weak interface between carbon fibers and polymer matrix in carbon fiber reinforced polymer composites (CFRCs). We have carried out direct growth of CNTs on carbon fibers by using two different catalytic chemical vapor deposition (CVD) processes, namely the conventional CVD process based on catalytic thermal decomposition of ethylene and the oxidative dehydrogenation reaction between acetylene and carbon dioxide. The effect of various CVD growth parameters, such as temperature, catalyst composition and process gas mixture, was for the first time systematically studied for both processes and correlated with the mechanical properties of carbon fibers derived from single-fiber tensile tests. The growth temperature was found to be the most critical parameter in the presence of catalyst particles and reactive gasses for both processes. The oxidative dehydrogenation reaction enabled decreasing CNT growth temperature as low as 500 C and succeeded to grow CNTs without degradation of carbon fiber's mechanical properties. The Weibull modulus even increased indicating partial healing of present defects during the CVD process. The new insights gained in this study open a way towards simple, highly reproducible and up-scalable process of grafting CNTs on carbon fibers without inducing any damages during the CVD process. This represents an important step towards CNT-reinforced CFRCs with higher damage resistance. (C) 2014 Elsevier B.V. All rights reserved.