The NeXT mission has been proposed to study high-energy non-thermal phenomena in the universe. The high-energy response of the super mirror will enable us to perform the first sensitive imaging observations up to 80 keV. The focal plane detector, which combines a fully depleted X-ray CCD and a pixellated CdTe detector, will provide spectra and images in the wide energy range from 0.5 keV to 80 keV. In the soft gamma-ray band up to ~1 MeV, a narrow field-of-view Compton gamma-ray telescope utilizing several tens of layers of thin Si or CdTe detector will provide precise spectra with much higher sensitivity than present instruments. The continuum sensitivity will reach several times 10^(-8) photons/s/keV/cm^(2) in the hard X-ray region and a few times10^(-7) photons/s/keV/cm^(2) in the soft gamma-ray region.