The flux motion has been investigated in a Tl 2 Ba 2 CaCu 2 O 8 thin film by transport measurements with a weak applied magnetic field perpendicular to the (a,b) plane ranging from 20 to 300 mT. We have found a well defined line T * (H) separating ohmic from non ohmic behaviour in the H-T * diagram. This line is well described by l - t * ∼ H 2 / 3 where t * = T * /T c and T c is the zero magnetic field transition temperature. Above T * (H), a thermally activated resistance is observed. Our experimental results clearly indicate that the activation energy is well approximated by U(T,H) ∼ [l-(T/T c )] 3 / 2 /H both below and above the T * (H) line in the H-T * diagram. The nonlinear current dependence of the activation energy U(T,H,I) is extracted from I-V characteristics, and it is found that U(T,H,I) = U(T,H) ln(I 0 /I). Satisfactory agreement is found between our results and recent models which take into account a periodic logarithmic-like pinning potential.