We used local AC-susceptibility and global DC magnetization measurements to determine the magnetic phase diagram of two HgBa 2 CuO 4 + δ single crystals with T c =95 and 89.9 K, respectively. The corresponding lines for the more anisotropic crystal (T c =89.9K, crystal A) lie lower than those of the nearly optimally doped crystal (T c =95K, crystal B). The irreversibility line (IL) decreases exponentially in the temperature range 20=<T=<T * . At T * =82 and 88 K the IL change slope and varies with a power law up to the T c . Certain features in these measurements are also discussed.