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The daily global solar radiation data obtained from three Libyan locations, every one of them, it's located in differentregion,(Sabha- desert region), (Ghdames-middle region) and (Tripoli-Mediterranean region) were used to establish a relationship between daily diffuse fraction and daily clearness index K-T. This relationship was compared with that established by Liu & Jordan, Stanhill, Choudhury, Erbs, and used to derive a correlation for the average daily diffuse fraction. Solar radiation and sunshine duration are intimately related phenomena, which was used to study the equation related of average daily radiation to the extraterrestrial radiation for location and average fraction of possible sunshine hours. Moreover the daily clearness index were calculated and the daily clearness index was used to estimate the frequency of occurrence of days with different values of K-T and the cumulative frequency of occurrence of those days. Finally, the relationships for estimating the beam and diffuse components of daily global radiation were obtained using the previous mentioned author's model. (C) 2013 The Authrs. Published by Elsevier B.V.