A design approach for observers using multiple-integrals is presented for descriptor systems, which allows the authors to decouple or attenuate measurement output disturbances. Design schemes for both pure integral observers and proportional integral observers are investigated. Measurement noise and input disturbances are also simultaneously taken into account in the design. A systematic design procedure for a causal or normal multiple-integral observer is addressed, which can be implemented conveniently using Matlab software. The considered disturbance may be unbounded, which means that the presented design approach is suitable for more general cases. Moreover, the system state, together with the disturbance vector and its finite time derivatives can be simultaneously estimated. The proposed design has great potential for application to control problems, such as those in diagnosis or observer-based control. In addition, it also has good estimation robustness and can be directly applied to normal systems. Simulation results show a satisfactory tracking performance as compared to the results obtained for descriptor systems.