This chapter discusses the unknown input estimation problem for a class of time-delay systems with two non-commensurate delays, \(\tau \) and h, in both the state and output vectors. Due to the presence of non-commensurate delays, the design of an unknown input observer is more complicated than the one considered in Chap. 5. We provide discussions on their designs as well as some open problems to be considered in the future. To express the unknown input in its entirety, we impose some constraints on output matrices \(C_d\) and \(C_h\) . We then show that we can obtain a disturbance-free time-delay system with two non-commensurate time delays. The unknown input d(t) also contains a generalized functional of the form \(z_{\tau h}(t)=Fx(t)+F_dx(t-\tau )+F_hx(t-h)\) . Thus, the estimation of d(t) rests with the successful design of a generalized functional observer to estimate \(z_{\tau h}(t)\) .