A comparison of different catalysts (Ni, Co, Fe/Mo) has been performed in order to minimize the growth temperature for single-walled carbon nanotubes (SWCNTs). Dense SWCNT networks have been synthesized by thermal chemical vapor deposition (CVD) at temperatures as low as 600 degreesC using Ni catalyst layers of approximately 0.2 nm thickness. The dependence of the SWCNT growth on the most important parameters will be discussed exemplarily on the Ni catalyst system. On the basis of experimental observations, a phenomenological growth model for CVD synthesis of SWCNTs is proposed which is based on the interactions between the catalyst and its support. Further, it is suggested that only surface diffusion of hydrocarbons on the catalyst support or along the CNTs can explain the fast growth rates of SWCNTs during CVD synthesis.