This thesis has been dedicated to the study of derivative properties obtained from equations of state. The derivative properties are dependent on first or second order temperature or density derivatives of the principal thermodynamic surface. This means that the inaccuracy of the principal surface is easily revealed by these properties. The derivative properties used in this study were: - Isochoric heat capacity, - Isobaric heat capacity, - The Joule – Thomson, - The speed of sound, - The reduced bulk modulus. The real behavior of pure component properties derived from high accuracy multiparameter equations of state fitted to a large number of experimental data has been studied. The objective was to find general behavior among different substances. If there is a general behavior this would be helpful in the development of new and better functional structures for the description of thermodynamic properties. The isochoric heat capacity was found to have a regular behavior. Another objective of the thesis has been to investigate the representation of derivative properties obtained from some model equations of state. Those equations were: - Redlich – Kwong, - Soave - Redlich – Kwong, - Peng – Robinson, - SPHCT, - SAFT. The derived properties from the model equations for both pure substances and mixtures were compared to those from the high accuracy equations. All equations were found to give very poor representations of the isochoric heat capacity. In light of the poor estimation of the isochoric heat capacity obtained from model equations this behavior could serve as a tool in the further development of equations of state. In order to obtain reference data for mixtures new thermodynamic relationships for derivative properties have been developed based on the Extended Corresponding States theory. The new relationships were found to give excellent descriptions of derivative properties for mixtures.