Abstract: It is especially important for analysis and design of distributed parameter systems (DPS) to study their controllability and observability but is also very difficult because of the distribution characteristics of DPS.In this paper,based on the spectrum de composition principle,the concepts of approximate controllability and observability of DPS have been proposed and their criteria for linear DPS have also been studied by using orthogonal function approximate technique.For two typical cases the approximate controllability and observability criteria of the systems have been given,in which the actuators and the sensors are placed in different positions.The proposed method is simple,and easy for application to analysis and synthesis of DPS.