The widely used integral-equation approach for identification of continuous systems is investigated. Attention is focused on the initial condition problem which has been puzzling many researchers. A new calculation procedure for the multiple integrations of the system signal derivatives is proposed and a new integral-equation approach is proposed for which the initial conditions need not be identified as unknown parameters. Therefore, the burden of the identification algorithms can be greatly reduced compared to conventional methods. Discussions on the unification of the integral-equation approach with the other methods are also provided.