Mechanisms for converting electrical energy into mechanical energy are essential for the design of nanoscale transducers, sensors, actuators, motors, pumps, artificial muscles, and medical microrobots. Nanometre-scale actuation has to date been mainly achieved by using the (linear) piezoelectric effect in certain classes of crystals (for example, quartz), and 'smart' ceramics such as lead zirconate titanate. But the strains achievable in these materials are small--less than 0.1 per cent--so several alternative materials and approaches have been considered. These include grafted polyglutamates (which have a performance comparable to quartz), silicone elastomers (passive material--the constriction results from the Coulomb attraction of the capacitor electrodes between which the material is sandwiched) and carbon nanotubes (which are slow). High and fast strains of up to 4 per cent within an electric field of 150 MV x m(-1) have been achieved by electrostriction (this means that the strain is proportional to the square of the applied electric field) in an electron-irradiated poly(vinylidene fluoride-trifluoroethylene) copolymer. Here we report a material that shows a further increase in electrostriction by two orders of magnitude: ultrathin (less than 100 nanometres) ferroelectric liquid-crystalline elastomer films that exhibit 4 per cent strain at only 1.5 MV x m(-1). This giant electrostriction was obtained by combining the properties of ferroelectric liquid crystals with those of a polymer network. We expect that these results, which can be completely understood on a molecular level, will open new perspectives for applications.