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A study of the cycles of a lithium bromide–water absorption chiller with two-stage absorption and three-stage generation of a working substance vapor with an associated mass flow with different supply of the cooling medium to the apparatus has been carried out. The temperature of the heating source necessary for the implementation of the actual thermodynamic cycle of the Lithium Bromide– Water Absorption Chiller (LBWAC) and the most effective thermodynamic cycle has been determined. A comparative analysis of the cycle understudy with the sample cycle (one-stage cycle) LBWAC is carried out. Despite the lower values of the coefficient of performance (COP), the cycle under study provides a doubling of the cooling capacity of the machine, at the same flow rate of the heating source, which is an advantage when the flow rate of the heating source is limited. This circumstance is explained by the fact that in LBWAC with multi-stage absorption and generation, the heating source sequentially passes through three generator stages. Therefore, the degree of cooling in the chiller with the considered cycle is three times higher than this value of a single-stage LBWAC