The rounding of the transition curve is measured for superconducting bismuth films in a perpendicular magnetic field. The contribution of the fluctuating superconducting wave function to the conductivity above Tc in an applied magnetic field is calculated with a simple model. The allowed states of the fluctuations are cylinders in momentum space. During their life time the fluctuating superconducting electrons can be accelerated by an electrical field and contribute to the conductivity. Experiment and theory are in fair agreement. We obtain some information about the Pauli spin paramagnetism of the electrons. © 1969 Springer-Verlag.