The Part II. contains 7 chapter (9 - 15). Theoretical Background chapter shows the basis of mathematical modeling. In the Chapter 10., the methodology of mathematical diagnostic modeling is introduced. The Chapter 11. shows two real examples of the mathematical modeling. One of them is the pneumatic brake system of the helicopter Mi-8 HIP and its linearized mathematical diagnostic model. Another is the starter engine Al-9V and its non-linear thermodynamic mathematical model. In the Chapters 12, 13, 14 and 15, possibilities of application - diagnostic investigations, state-estimation, operational management and investigation of the manufacturing anomalies' effects - are shown. Applications mentioned above are illustrated by real examples using mathematical models set up in the Chapter 11.