The paper describes instruments for solar imaging XUV spectroscopy -- the TEREK-C telescope array and the RES-C spectroheliograph mounted on board the Russian-Ukrainian CORONAS-I satellite (launched on March 2, 1994). The CORONAS project is carried out under scientific guidance of Prof. V.N. Oraevsky, director of the IZMIRAN (Troitsk, Moscow region, Russia) -- leading institute of this project. The instruments were intended to obtain high resolution solar images and spectra from the transition region and the corona of the Sun within the temperature range of 105 - 107 K. The optical design of the TEREK telescope array includes two Herschelian XUV-telescopes with Mo-Si multilayer mirrors: the first one with 3 whole-Sun spectral channels (reflection peaks at (lambda) equals 13.2, 17.5 and 30.4 nm, angular scale 4.7'), the second channel -- with 4 mirrors, each covering 1/4 of the Sun ((lambda) equals 17.5 nm, angular scale 1'). The RES-C spectroheliograph has five measuring channels with a whole-Sun field of view: two XUV channels with orthogonal dispersion planes, equipped with grazing incidence gratings and multilayer mirrors to obtain high resolution spectral images in the 19.2 - 20.1 nm band (spectral resolution 2 (DOT) 10-4 nm/pix, angular scale 4.5'), two MgXII channels having narrow-band imaging systems with orthogonal dispersion planes for the 0.841 - 0.843 nm spectral band, equipped with Bragg crystal spherical mirrors, and one FeXXV imaging system with a ring Bragg crystal mirror for the 0.184 - 0.188 nm spectral band. Two types of image detectors were designed with the use of CCD-matrices (1024 X 1152 elements) and image intensifiers (with an open microchannel plate and a luminescent converter). The paper presents a detailed description of the overall structure, electronic design and the main characteristics of the instruments, preliminary results of flight functioning of the TEREK-C and RES-C instruments and examples of the images and spectra of the Sun obtained in the experiment.