Highly deformable and electrically conductive fibres with multiple functionalities may be useful for diverse applications. Here we report on a supercoil structure (i.e. coiling of a coil) of fibres fabricated by inserting a giant twist into spandex-core fibres wrapped in a carbon nanotube sheath. The resulting supercoiled fibres show a highly ordered and compact structure along the fibre direction, which can sustain up to 1,500% elastic deformation. The supercoiled fibre exhibits an increase in resistance of 4.2% for stretching of 1,000% when overcoated by a passivation layer. Moreover, by incorporating pseudocapacitive-active materials, we demonstrate the existence of superelastic supercapacitors with high linear and areal capacitance values of 21.7 mF cm-1 and 92.1 mF cm-2, respectively, that can be reversibly stretched by 1,000% without significant capacitance loss. The supercoiled fibre can also function as an electrothermal artificial muscle, contracting 4.2% (percentage of loaded fibre length) when 0.45 V mm-1 is applied.