Abstract We have investigated the temperature dependence and applied magnetic-field dependences of critical current densities J c( H, T) and the irreversibility lines H irr( T) obtained from the magnetization measurements in HgBa 2(Ca 1- x Sr x ) 2Cu 3O 8+ δ and Hg 0.5Tl 0.5Ba 2(Ca 1- x Sr x ) 2Cu 3O 8+ δ . J c( H, T) and H irr( T) of Hg 0.5Tl 0.5Ba 2(Ca 1- x Sr x ) 2Cu 3O 8+ δ are found to be higher than those of HgBa 2(Ca 1- x Sr x ) 2Cu 3O 8+ δ , indicating that the Tl substitution at Hg sites provides additional flux pinning. J c( H, T) has been analyzed using the flux-creep model. J c( H, T) in magnetic fields above 1 T is well described by the flux-creep model. However, the thermal activation energy estimated by fitting the data to the flux-creep model shows different behaviors above and below about 65 K for both HgBa 2(Ca 1- x Sr x ) 2Cu 3O 8+ δ and Hg 0.5Tl 0.5Ba 2(Ca 1- x Sr x ) 2Cu 3O 8+ δ . Also, in H irr( T) a crossover from a power-law temperature dependence above 65 K to a more rapid dependence below 65 K is observed in both samples. Although the origin of such a crossover in H irr( T) and J c( H, T) is not clear, the two phenomena are considered to be closely related.