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The purpose of the present article is to calculate the internal friction of binary substitution-al alloys in different states of order by the application of the general thermodynamical theory of internal friction of linear type. To begin with, free energies are deduced for specimens under the action of a uniform stress, which, so far as the degree of order is concerned, is not in equilibrium. In this paper two mechanisms, the preferential distribution of atom-pairs and the change of degrees of short range order that give rise to the internal friction are suggested. In either case the internal friction is found to be proportional to the first and second power of (1-S), where is the degree of long range order. Thus, in the state of complete order, the internal friction would vanish, whereas it would be a maximum in the state of complete disorder. Theoretical results are in perfect accord with Nowick's data for the complete order in the Ag-Zn alloys and with the work of the Artman for the ordered states of β-brass. However, according to the theory, these experimental findings seem to indicate that it is the ordering pairs rather than the change of short range order that appear to be the cause of these two internal friction peaks.