We present the optical design of high-resolution monochromators for the utilization of the radiation from a FEL at 40 and 10 nm, in the framework of a proposal made from Elettra Synchrotron (Trieste, Italy) to the Italian Ministry of Education, Universities and Research for the construction and operation of an ultra-high brilliance source in the UV and x region. Since the FEL emission is expected to be highly monochromatic (X/A2l0000), a monochromator is useful only if able to provide a spectral resolution higher than the intrinsic FEL resolution (X/&>100000). Two systems are presented: 1) normal-incidence configurations with multilayer-coated optics; 2) grazing-incidence configurations with a plane grating operated in conical diffraction. Normal-incidence configurations have very high spectral resolution, but the spectral band of operation is limited by the multilayer coating, so optics with different coatings have to be used when the FEL is tuned within the spectral region of operation. Configurations in conical diffraction have also very high resolution, higher efficiency and a wide spectral band of operation.