The present work deals with modeling the zenith luminance, L-z, on Madrid cloudless skies, from solar elevation and diffuse illuminance on a horizontal surface. Two different approaches are followed. The first approach has been to compare the mean experimental zenith luminance values calculated at every 5 interval of solar elevation with the corresponding values obtained from the equations given for the five cloudless sky standards proposed by Kittler et al. [Final report of the American Slovak grant project US SK 92 052]. In this approach, standard sky V.5 was found to give the best fit to the experimental data. Excellent agreement was observed up to a solar elevation of about 40, although a clear deviation between the predicted and experimental values was obtained for higher solar elevations. Considering the importance of accurate modeling of the zenith luminance and in view of the results obtained with the first approach, a second method was tried. Different fits to the experimental data were tested. It was observed that a simple inverse equation, relating the ratio of the zenith luminance to the diffuse illuminance to the cosine of the solar elevation gives a good fit of the experimental data for all solar elevations. The percentage mean bias errors (MBE) and root mean square errors (RMSE) for L-z, as estimated from the above mentioned inverse equation are -0.32% and 9.38%, while using the equation for standard sky V.5 in the first approach, the MBE and RMSE are 7.04% and 19.01%, respectively. Although other fits are somewhat better than the inverse equation mentioned, the inverse equation is preferred because it contains only two empirically determined coefficients.