This paper addresses the identification of the parameters of a nonlinear constitutive law from indentation tests. The identification problem is considered as a constrained minimization problem and the gradient is computed using the adjoint state method, in spite of the difficulties of the underlying contact problem. This provides a general framework to perform optimization in some problems involving contact conditions and nonlinear material behaviour. The case of a Maxwell viscoelastic and a Norton-Hoff elastoviscoplastic constitutive law are treated extensively and a series of numerical identification examples are shown.