This publication is the first part of a book that deals with mathematical modelling of processes, their dynamical properties and dynamical characteristics. The need of investigation of dynamical characteristics of processes comes from their use in process control. The second part of the book will deal with process identication, optimal, and adaptive control. The aim of this part is to demonstrate the development of mathematical models for process control. Detailed explanation is given to state-space and input-output process models. In the chapter Dynamical properties of processes, process responses to the unit step, unit impulse, harmonic signal, and to a random signal are explored.