Extremely high dynamic range is required if magnetometer SQUIDs are to be operated while in motion in the earth's field. We have developed an HTS SQUID gradiometer system that uses active shielding and an adaptive signal processing algorithm to achieve the necessary dynamic range. An array of four thin-film SQUIDs with flux transformers is configured to form two orthogonal magnetometers and a single-axis gradiometer with a baseline of 10 cm. External field changes are cancelled by a three-axis Helmholtz coil set, driven by integral feedback from the SQUIDs, which surrounds the array. A real time adaptive balancing algorithm corrects for gradient offset, electronics scaling errors, sensor misalignments and uniformity errors in the Helmholtz coils. For outside use, light RF shielding is provided by thin layers of Al foil.In laboratory tests, intrinsic noise levels of 20 pT m Hz (1 Hz) and 0.3 pT m Hz (white) were measured. In field trials, the Helmholtz coils provided a shielding factor, for uniform fields, of 50-60 dB (0.1-10 Hz) during roll, pitch and yaw rotations of up to 5 . Adaptive balancing reduced gradient noise to the ambient background level of 80 pT m Hz (1 Hz) and 1 pT m Hz (white), whilst in motion.