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This paper investigates the econometric application of a flexible functional form of Generalised Leontief function. We will focus our attention on econometric techniques that are used to analyze the interrelated demands for labour, capital and other inputs in production processes. In particular, we begin with an historical overview of the literature on the demand for factors of production, beginning with the famous Cobb-Douglas model and constant elasticity of substitution (CES) and moving with the application of Generalised Leontief function using data from the Greek industry