The regression coefficients of a modifiedÅngström formula, initially postulated as being constant under all climatic conditions, have with widespread use been shown to vary not only spatially but also due to variable sunshine duration conditions. Daily sunshine duration and solar radiation data sets were analysed in order to assess the variations of the coefficients a and fa in the formulaK/Ko= a +bn/Nunder differing conditions of relative sunshine duration in South Africa. The results show that whereas coefficient a tends toward being linearly related to sunshine duration, coefficientbexhibits a hyperbolic type relationship. The statistical relationships between both coefficients and sunshine duration are, however, weak. The study also shows that the equations suggested by Rietveld for deriving the coefficients a andbare not valid under South African conditions.S. Afr. J. Plant Soil1986, 3: 45–48