An approximation approach to the identification of stable continuous-time, possibly infinite dimensional systems is studied. For this purpose, concrete exponential Leg-endre series methods are proposed and analysed here for the L1and L2approximations of continuous-time systems. Rate of approximation results are given for the proposed methods for an important class of delay systems. The proposed exponential Legendre series method for the L2approximation has a certain optimal rate of approximation property for this class of delay systems. These results show that exponential Legendre series techniques have promising properties in connection with the L1and L2identifications of stable continuous-time systems. The proposed L1identification method has a direct application to the robust design of control systems.