In two recent papers Enders and Lee (2008) and Becker et al. (2006) provide Lagrange multiplier and OLS de-trended unit root tests, and stationarity tests, respectively, which incorporate a Fourier approximation element in the deterministic component. Such an approach can prove useful in providing robustness against a variety of breaks in the deterministic trend function of unknown form and number. In this paper, we generalise the unit root testing procedure based on local GLS de-trending proposed by Elliott, Rothenberg and Stock (1996) to allow for a Fourier approximation to the unknown deterministic component in the same way. We show that although the resulting unit root tests possess good finite sample size and power properties, their limit null distributions are undefined.