Lead and tin nanotubes were synthesized by electroless deposition in a nanoporous polymer membrane without sensitization, activation or a reducing agent. A thick Pb or Sn layer is evaporated on one side of the membrane and provides the metallic ions needed to grow the tubes in an aqueous solution. The nanotubes' geometry and composition were investigated by means of electron microscopy, energy dispersive x-ray spectroscopy and ultramicrotomy. Electrical measurements obtained on such superconducting nanotubes are compared with solid wire characteristics. This spontaneous growth could explain some recent results obtained on superconducting nanowires showing an anomalous long-range proximity effect.