A systematic study of the weak link behaviour for (Cu 0.5 Tl 0.5− x K x )Ba 2 Ca 2 Cu 3 O 10− δ (x=0, 0.25) superconductors samples has been carried out using electrical resistivity and AC-susceptibility techniques. The K-doped (Cu 0.5 Tl 0.5− x K x )Ba 2 Ca 2 Cu 3 O 10− δ samples were synthesized by solid-state reaction method. In magnetic susceptibility measurements, the real (χ′) and imaginary (χ″) parts of the magnetic susceptibility of (Cu 0.5 Tl 0.5− x K x )Ba 2 Ca 2 Cu 3 O 10− δ (x=0, 0.25) samples were measured as a function of temperature under various DC-magnetic fields up to 172Oe. It is observed from these studies that the magnitude of the diamagnetism is substantially enhanced by K-doping. The possible reasons for the enhanced magnitude of diamagnetism have been investigated. It is observed from in-field magnetic measurements that the inter-grain coupling is improved with the K-doping. It is concluded from these studies that potassium atoms appearing at the crystal boundaries enhance inter-grain coupling and pinning mechanism in K-doped (Cu 0.5 Tl 0.25 K 0.25 )Ba 2 Ca 2 Cu 3 O 10− δ superconductors.