Within the framework of the Entropy-free Thermodynamic of Processes (ETIP) developed by J. Meixner, it is investigated for what type of fluid or solid systems the Clausius-Duhem-Inequality (CDI) will hold for the thermostatic entropy sth. The following statements will be proved: 1. The CDI holds for processes in simple thermodynamic systems of the differential type with complexity 1 or 2. In these cases the CDI is a consequence of the fundamental inequality of ETIP. 2. The CDI cannot hold for processes in simple thermodynamic systems of the integral type with complexity 1. 3. The CDI may or may not hold for processes in simple thermodynamic systems of the integral type with complexity 2.