We investigate a new type of resonant behaviour in the 1D hot-electron ballistic transport in nanostructures. The resonances are manifested by sharp increases in the rate of optical phonon generation and are accompanied by sharp drops in the overall current. They occur whenever the separation between a pair of levels of transverse quantization is equal to the energy of an optical phonon, h(cross) omega ₀, and a condition for generation of optical phonons eV>h(cross) omega ₀, is met, where V is the voltage bias across the conductor. We calculate the rate of energy transfer from the electrons to phonons. The ratio between the decrease in electric current power and the rate of energy transfer from electrons to phonons appears to be linearly proportional to the voltage bias.