L. Amour, R. Brummelhuis, J. Nourrigat Resonances of the Dirac Hamiltonian in the non relativistic limit (58K, Latex) ABSTRACT. For a Dirac operator in $\R ^3$ with an electric potential behaving at infinity like a power of $ | x | $, we prove the existence of resonances and we study, when $c\rightarrow + \infty $, the asymptotic expansion of their real part, and an estimation of their imaginary part, generalizing an old result of Titchmarsh.