We have developed high-critical-temperature radio-frequency Super conducting QUantum Interference Devices (SQUIDs) with step-edge grain-boundary Josephson junctions and large flux focusers. These planar devices were fabricated from epitaxial YBa2Cu3O7 films and operated in the magnetometer and first-order gradiometer configurations while immersed in liquid nitrogen. At the temperature of 77K, we have attained a magnetic field resolution for the magnetometer better than 200 fT/Hz1/2 down to less than 1 Hz, i.e., over the low signal frequency range important for medical diagnostics. The results to date show a high promise for biomagnetic diagnostics. For the first time, we recorded the evoked responses from human brains using a high-temperature magnetometer and a first-order electronic gradiometer channel simultaneously. These results were obtained in a magnetically shielded room. An improvement in the magnetic field resolution by another order of magnitude is possible and probable.