Abstract: This paper estimates the Spectral approximation by Spectral Tau and Spectral Least Squares Method for the first order Neutral Delay Differential Equation (NDDE). Here the NDDE is reduced into advection Equation to determine Spectral solutions. The effects on different types of basis are compared with numerical solution of NDDE. The Legendre and Chebyshev Basis generate much superior results than the Mixed Fourier Basis.