Research in stretchable conductors is fuelled by diverse technological needs. Flexible electronics, neuroprosthetic and cardiostimulating implants, soft robotics and other curvilinear systems require materials with high conductivity over a tensile strain of 100 per cent (refs 1-3). Furthermore, implantable devices or stretchable displays(4) need materials with conductivities a thousand times higher while retaining a strain of 100 per cent. However, the molecular mechanisms that operate during material deformation and stiffening make stretchability and conductivity fundamentally difficult properties to combine. The macroscale stretching of solids elongates chemical bonds, leading to the reduced overlap and delocalization of electronic orbitals(5). This conductivity-stretchability dilemma can be exemplified by liquid metals, in which conduction pathways are retained on large deformation but weak interatomic bonds lead to compromised strength. The best-known stretchable conductors use polymer matrices containing percolated networks of high-aspect-ratio nanometre-scale tubes or nanowires to address this dilemma to some extent(6-11). Further improvements have been achieved by using fillers (the conductive component) with increased aspect ratio, of all-metallic composition(12), or with specific alignment (the way the fillers are arranged in the matrix)(13,14). However, the synthesis and separation of high-aspect-ratio fillers is challenging, stiffness increases with the volume content of metallic filler, and anisotropy increases with alignment(15). Pre-strained substrates(16,17), buckled microwires(18) and three-dimensional microfluidic polymer networks(19) have also been explored. Here we demonstrate stretchable conductors of polyurethane containing spherical nanoparticles deposited by either layer-by-layer assembly or vacuum-assisted flocculation. High conductivity and stretchability were observed in both composites despite the minimal aspect ratio of the nanoparticles. These materials also demonstrate the electronic tunability of mechanical properties, which arise from the dynamic self-organization of the nanoparticles under stress. A modified percolation theory incorporating the self-assembly behaviour of nanoparticles gave an excellent match with the experimental data.