The zenith luminance has been measured at Madrid for skies with a cloud cover of 7-8 oktas and experimental mean 15-min values of L-z have been obtained. Among the most accurate fits to the data, a 2nd degree polynomial for L-z against tan(alpha) is the most simple. When only data for a cloud cover of 8 oktas are used a similar fit is obtained, but for a smaller coefficient of correlation, due to the smaller amount of data. A linear, second degree, or power dependence for L-z against sin(alpha )obtained by other researchers, does not give the best fit for our data. (C) 2000 Elsevier Science Ltd. All rights reserved.