Superconducting hot electron bolometer mixers are now a competitive alternative to Schottky diode mixers in the terahertz frequency range because of their ultra wideband (from millimeter waves to visible light), high conversion gain, and low intrinsic noise level. High Tc superconductor materials can be used to make hot electron bolometers and present some advantage in term of operating temperature and cooling. In this paper, we present first a model for the study of superconducting hot electron bolometers responsivity in direct detection mode, in order to establish a firm basis for the design of future THz mixers. Secondly, an original process to realize YBaCuO hot electron bolometer mixers will be described. Submicron YBaCuO superconducting structures are expitaxially sputter deposited on MgO substrates and patterned by using electron beam lithography in combination with optical lithography. Metal masks achieved by electron beam lithography are insuring a good bridge definition and protection during ion etching. Finally, detection experiments are being performed with a laser at 850 nm wavelength, in homodyne mode in order to prove the feasibility and potential performances of these devices.