Theoretical analysis of entropy generation and availability destruction of "n" similar cocurrent or countercurrent heat exchangers connected in series are presented. A criterion for comparing the relative performance of any number of in-series connected similar heat exchangers is developed. The effect of different influencing parameters such as the number of connected heat exchangers, the individual effectiveness of each unit, the heat capacity rate ratio and flow arrangement on the quality of heat exchange are presented. It is found that, the maximum of availability destruction (maximum entropy generation) for in-series-connected similar cocurrent heat exchangers is obtained at epsilon* = 1/(1 + delta). However, for counter-current heat exchangers connected in-series; epsilon(n)* = 1/(Sigma(i=o)(n) delta(i/n)). This analysis might be useful for a proper choice of the number of heat exchangers to be connected together and the choice for the best operating conditions.