  According to the crystal structure of MgB$_{2}$ and band structure
calculations quasi-two-dimensional (2D) boron planes are responsible for the
superconductivity. We report on critical fields and resistance measurements of
30 nm thick MgB$_{2}$ films grown on MgO single crystalline substrate. A linear
temperature dependence of the parallel and perpendicular upper critical fields
indicate a 3D-like penetration of magnetic field into the sample. Resistivity
measurements, in contrast, yield a temperature dependence of fluctuation
conductivity above T$_{c}$ which agrees with the Aslamazov-Larkin theory of
fluctuations in 2D superconductors. We consider this finding as an experimental
evidence of two-dimensional nucleation of superconductivity in MgB$_{2}$.
