Physical properties of d γ-symmetry Cooper pairs were theoretically investigated by assuming the dispersion relation of a simple square lattice with the nearest neighbor transfer integral and attractive interactions between the nearest neighbors. Calculated properties such as the energy gap, the density of states and the NMR relaxation time show highly anisotropic features. A possibility is discussed that d γ-symmetry super-conductivity realized by the nearest neighbor exchange interactions can explain the properties of high- T c ceramic superconductors recently discovered. It is also shown that exchange interactions determined in insulating phases can explain high superconducting transition temperatures in metallic phases.