This chapter examines the assumptions that must be made for the observer schemes described earlier in the book to be applicable. (These amount to relative degree one minimum phase limitations on the transfer function matrices relating the unknown fault signals to the measurements.) This chapter explores ways of obviating these limitations, at the expense of creating cascaded observer structures. The components of the cascade will be observer formulations taken from earlier chapters, and explicit constructive algorithms will be given to ensure the overall scheme can still accurately estimate actuator faults in the case where the relative degree between the faults and the measurements is greater than or equal to two. The advantages that these schemes offer over traditional linear methods (particularly Unknown Input Observers) will be demonstrated.