The main aim of this work is divided into four objects. These are summarized as follows: The first objectives, is to study the ordinary differential equations with deviating arguments. The second objectives, is to derive an estimate of the magnitude of the solutions for special types of linear and nonlinear ordinary differential equations with deviating arguments in order to solve them by any suitable methods. The third objectives, is to devote the existence of a unique bounded solution for special types of the partial differential equations with deviating arguments. The fourth objectives, is to give an estimate of the magnitude of solutions for special types of 1st order and 2nd order partial differential equations with deviating arguments.