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Two different concepts for gradiometer formation were tested applying high-temperature rf SQUIDs operated at 77 K in liquid nitrogen. All gradiometer systems are fully based on magnetometers. The first concept applies a compensating magnetometer at different positions to actively cancel the magnetic field at the location of other magnetometers. These magnetometers were arranged in an axial direction. In parts, a system of superconducting plates was used to align the relative magnetic orientation of the magnetometers. The outputs of these sensors were used to form a highly balanced electronic gradiometer. The second concept is based on electronic noise cancellation. A set of three magnetometers arranged in an axial direction was used to form an electronic second-order gradiometer. Different types of reference systems based on HTS-SQUID magnetometers and fluxgate sensors were applied to the gradiometer signal for achieving a high common mode rejection of the environmental disturbances. The performance of the different systems is demonstrated in a magnetically unshielded environment as well as in a shielded environment and the common mode rejection of homogeneous magnetic fields is measured. To demonstrate the performance of the systems, biomagnetic measurements have been performed in shielded and unshielded environments.