  A potential model to describe the total cross section of nuclear fusion
reactions at low energies is proposed. It is shown that within an approach with
a simple, single barrier potential a satisfactory description of data is
hindered, while with models with more complex interactions, e.g., with
two-barrier potentials, a good description of data can be achieved in a large
interval of colliding nuclei and center of mass energies. In particular, the
two-barrier model allows to describe data at low, sub-barrier energies where
data exhibits a steep falloff of the cross section. It is also shown that the
position of the two barriers is almost independent up on masses of colliding
nuclei. Comparison with available experimental data is presented as well.
