This paper deals with the observability problem of a sort of singular systems with commensurate time-delays in the trajectories of the system, in the time derivative of the trajectories (neutral terms), and in the output system. By using a recursive algorithm, sufficient conditions (easy testable) are proposed for guaranteeing the backward and the algebraic observability of the system. This condition implies that the trajectories of the system can be reconstructed by using the actual and past values of the system output.