Basically, the solution of estimating the time delay between two signals received at two spatially separated sensors consists of cross correlating the sensor's output and using the time argument that corresponds to the maximum peak as the time delay estimate. To improve the estimation process, various optimum or heurestic filters have been suggested. Design of these filters requires the exact knowledge of the input spectra which is practicglly difficult. It would therefore be useful if fixed filters were specifically designed to have good performance over entire classes of input spectral densities. In this paper, robust solutions to the two optimum filters derived by Hassab and Boucher to estimate the time delay are derived. Explicit solutions for the c-contaminated power spectral densities (PSD's) will be given. Numerical examples are given to illustrate the benefits of using robust filters in time delay estimation (TDE). Simulation results are also given. The results obtained show that robust filters are the saddle point solutions for the c-contaminated spectral classes and ensure the advantages of robustness.