In this paper, we investigated detailed behavior of novel HTS-dc-SQUID gradiometers with ramp-edge Josephson junctions (JJs) in both an ac magnetic field and a dc magnetic field. In the both fields, the novel gradiometers shows the superior performance to the conventional YBa2Cu3O7−x (YBCO) HTS-dc-SQUID gradiometer and a bare HTS-dc-SQUID ring with bicrystal JJs concerning durability against entry and hopping of flux vortices, probably due to their differential pickup coils without a grain boundary and multilayer structure of the ramp-edge JJs. A robot-based compact HTS-SQUID NDE system utilizing the novel gradiometer was reviewed, and detectability of the system to detect non-through cracks in a carbon fiber reinforced plastic (CFRP)/Al double-layer structure was demonstrated. A new excitation coil in which the supplied currents flowed in the orthogonal directions was applied to detect cracks that oriented vertical and parallel to the baseline of the gradiometer.