We have been developing hard X-ray/soft gamma-ray imaging detectors for a next generation X-ray satellite mission, NeXT, proposed in Japan. The Hard X-ray Imager (HXI) onboard NeXT is located at the focal plane of the Hard X-ray Telescope (HXT) to achieve unprecedented sensitivities in the 10-80 keV energy band. It consists of multiple layers of double-sided silicon strip detectors followed by a double- sided CdTe strip detector. The Soft Gamma-ray Detector (SGD) onboard NeXT is a Compton camera consists of 20 layers of silicon pad detectors surrounded by CdTe pad detectors. Combined with a narrow field of view (0.5-4 deg) active BGO collimator and Compton kinematics, it achieves one order of magnitude better sensitivities in the 80-300 keV band. I will describe the development of silicon and CdTe detectors and low noise/low power front-end ASICs (Application Specific Integrated Circuits) commonly used in both instruments.