Ni–Co hydroxide nanosheets (NCHSs) were coated on buckypaper (BP) by a facile and one-step electrodeposition method for high-performance supercapacitor electrodes. The binary metal hydroxides show great superiority over the related single hydroxides. A novel sheet-on-tube hierarchical structure with a uniform distribution of Ni–Co hydroxides on BP shows great promise in supercapacitor applications. Such hybrid electrodes exhibit a high areal capacitance of 1.5 F cm⁻² (corresponding to 1725 F g⁻¹ based on the mass of active material), high rate capability and excellent cyclic stability. Based on the hybrid electrodes, ultrathin and highly flexible asymmetric supercapacitors were fabricated. The as-prepared asymmetric device shows high capacitance (0.3 F cm⁻² at a current density of 3 mA cm⁻²), low internal resistance (approx. 5 Ω for the whole device), excellent long-term cycle life (capacitance retention of 92% over 10 000 cycles), and high flexibility (negligible capacitance changes during large deformation), which makes it particularly well-suited for applications in next generation high-performance energy storage systems.