The effect of fluctuations on the transport and thermodynamic properties of
two-dimensional superconductors in a perpendicular magnetic field is studi
ed at low temperature T much less thanT(c0). The fluctuation conductivity i
s calculated in the framework of perturbation theory with the help of the u
sual diagram technique. It is shown that in the dirty case the Aslamazov-La
rkin, Maki-Thompson, and density of states contributions are of the same or
der. At extremely low temperature T/T-c0 much less than [H - H-c2(O)]/H-c2(
0) the total fluctuation correction to the normal conductivity is negative
in the dirty limit and depends on the external magnetic field logarithmical
ly delta sigma proportional to ln[H - H-c2(0)]. In the nonlocal clean limit
, the Aslamazov-Larkin contribution to conductivity is evaluated with the a
id of Helfand-Werthamer theory. The longitudinal and Hall conductivities ar
e found. The fluctuating magnetization is calculated in the one-loop and tw
o-loop approximations.