The isothermal magnetization hysteresis loops were measured for Tl₂Ba₂CuO₆ (Tl-2201) single crystals by using a SQUID magnetometer and a micro Hall sensor. In the temperature window from 15 to 30 K, the Hall sensor measurements for M(B) showed a second magnetization peak (SMP) at a peak field, B_sp, and an onset field, B_on. In this temperature region, the second peak appeared as a shoulder in the M(H) plots when measured by using SQUID. At a temperature of 20 K, time relaxation measurements for the time interval of 1–10⁴ s were carried out at different fields by using a Hall sensor. From these relaxation data, for both flux exit and entry, the activation barrier, U₀, and the creep exponent, μ, were separately calculated as a function of local field, B_z, by using the weak collective pinning theory. The variation of μ, and U₀ as a function B indicates that below the onset of the second peak field, B_on, the creep mechanism is an elastic process, but above it, a gradual transition to plastic creep takes place. At higher fields, μ and U₀ reduce sharply. This has been interpreted as a smooth transition to a 2D collective pinning state. These results are compared with that obtained in a double layer Tl compound, Tl₂Ba₂CaCu₂O₈ (Tl-2212),as well as other high-T_c materials.