Various morphologies of carbon nanotubes (CNTs) are grown catalytically on metal alloy probes and metal-oxide materials in counterflow diffusion flames using methane as fuel. It is found that multi-wall carbon nanotubes (MWNTs) are grown from metal-alloy probes while both MWNTs and single-wall carbon nanotubes (SWNTs) are obtained from the metal-oxide materials. CNT growth and morphologies are investigated as functions of local gas-phase temperatures, C-related species concentrations (e.g. C2H2, CO), sampling positions, C2H2 adding to the fuel, and probe compositions. CNTs grow optimally in non-sooty regions of the flames. C 2H2addition is found to promote direct synthesis of vertically well-aligned MWNTs with uniform diameters from Ni/Cr/Fe.