Optimum filters are used to enhance the performance of the generalized cross correlator (GCC) used in time delay estimators (TDE). The performance of these TDE can deteriorate considerably for deviations in the input power spectral densities (PSD's) from their assumed nominal values. In this pap-er we consider the bounded spectral classes of PSD's which are useful mode-ls when the input PSD's are not precisely known. For these classes, robust filters for TDE are derived for two optimum criterions separately. These criterions are maximizing the signal to noise ratio and minimizing the mean square error. The robust filters obtained achieve better performance for any inputs within the assumed PSD's. Numerical examples given illustrate the theoretical results.