In this paper, an analytical extension of the classical ideal Anderson-Schulz-Flory (ASF) distribution for the products of Fischer-Tropsch reactions is presented. The extension includes a description of enhanced product formation and re-adsorption and is therefore capable of describing real distributions with the known deviations from the ideal ASF distribution for C-1 and C-2 components and, by including the known double-ASF concept, the deviations of longer-chain hydrocarbons (C10+.). The model contains five dedicated parameters, each of which is associated with a particular characteristic of the product distribution. The developed equations are analytical solutions for the mole fractions y(n), and selectivities S-n, of product components, the average carbon number (n) over bar as well as for the sub-totals y(n+) and Sn+. Besides the flexibility and wide range of applicability of the extended ASF model, it allows simple and direct extraction of the relevant parameters from experimental data. These new distribution functions are considered to be valuable as a descriptive model for characterizing experimental data and as a basis for predictive models of product distribution for engineering applications. (C) 2015 Elsevier Ltd. All rights reserved.