We consider the inverse eigenvalue problems for stationary Dirac systems with differentiable self-adjoint matrix potential.The theorem of Ambarzumyan for a Sturm-Liouville problem is extended to Dirac operators,which are subject to separation boundary conditions or periodic (semi-periodic) boundary conditions,and some analogs of Ambarzumyan’s theorem are obtained.The proof is based on the existence and extremal properties of the smallest eigenvalue of corresponding vectorial Sturm-Liouville operators,which are the second power of Dirac operators.