  We test the prediction of the time variation of the fine structure constant
in the string dilaton model proposed by Damour and Polyakov. First, we analize
the dependence of all available observational and experimental data with the
fine structure constant variation. Furthermore, we obtain the prediction of the
time variation of the fine structure constant including the renormalization
group correction. Finally, we use the data set to perform a statistical
analyisis. This analysis enables us to determine that the the dilaton model is
in agreement with most of the data. Finally, constraints on the free parameters
of this model are obtained.

Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology;High Energy Physics - Theory