We report measurements of the magnetic field dependence of the resisti
ve transition in Tl2Ba2CuO6+delta for several crystals with transition
s in the range 15K less than or equal to T-c less than or equal to 62K
. The transition of the most overdoped sample (with the lowest transit
ion temperature) shifts monotonically to lower temperature with increa
sing field with no appreciable change in shape. The temperature depend
ence of the upper critical field (H-c2) inferred from these measuremen
ts does not have the classical BCS form [1]. The samples with higher t
ransition temperatures however do not show such simple behaviour, with
the transitions becoming systematically broader in a field as the tra
nsition temperature increases. These higher T-c samples develop a knee
-like structure in the transition at sufficiently high field. We discu
ss the similarities and differences between this knee and the sharp dr
op in resistance from an apparent normal state value seen for the lowe
st T-c sample, and the interpretation of this feature as a measure of
H-c2.