The structural, chemical, and electronic properties of epitaxial graphene films grown by thermal decomposition of the Si-face of a semi-insulating 6H-SiC substrate in an argon environment are studied by Raman spectroscopy, X-ray photoelectron spectroscopy and angle-resolved photoemission. It was demonstrated the possibility of fabrication of the gas and biosensors that is based on grown graphene films. The gas sensors are sufficiently sensitive to NO₂ at low concentrations. The biosensor operation was checked using an immunochemical system comprising fluorescein dye and monoclonal anti fluorescein antibodies. The sensor detects fluorescein concentration on a level of 1-10 ng/mL and bovine serum albumin- fluorescein conjugate on a level of 1-5 ng/mL. The proposed device has good prospects for use for early diagnostics of various diseases.