Single wall carbon nanotubes (SWNT) are model systems for the study of electronic transport in one-dimensional conductors. They are expected to exhibit strong electronic correlations and non-Fermi liquid behavior as suggested by recent experiments. The possibility to induce supercurrents through such molecular wires is a challenging question both for experimentalists and theoreticians. In this paper we show experimental evidence of induced superconductivity in a SWNT. This proximity effect is observed in a single 1 nm diameter SWNT, in individual cristalline ropes containing about 100 nanotubes and also on multiwalled tubes. These samples are suspended as strings between two superconducting electrodes (double layer Au-Re, Au-Ta or Sn film) at a distance varying between 100 and 2 000 nm. This allows their structural study in a transmission electron microscope. When their resistance is low enough, SWNT become superconducting with surprisingly high critical currents (in the micro-Ampere range for a single tube of normal state resistance 25 kΩ). This critical current, extensively studied as function of temperature and magnetic field, exhibits unusual features which are not observed in conventional Superconducting-Normal-Superconducting junctions and can be related to the strong 1D character of these samples. We also show evidence of a huge sensitivity of dc transport properties of the tubes to electromagnetic radiation in the radio-frequency range.Les nanotubes de carbone sont des systemes modeles pour l'etude du transport electronique a une dimension. Nous montrons experimentalement qu'il est possible d'induire de la supraconductivite dans ces fils moleculaires par effet de proximite. Les courants critiques des jonctions ainsi obtenues sont suprenants par leur amplitude, ainsi que leur dependance en temperature et en champ magnetique.