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An Ideal Adiabatic analysis of a Stirling cryocooler with multiple expansion stages has been presented previously. In this analysis the compression space and the various expansion spaces are adiabatic, the heat exchangers are isothermal and the regenerators are ideal. This paper is an extension of that analysis to evaluate the enthalpy losses associated with the interstage regenerators. The regenerator effectiveness is defined in terms of the total unidirectional heat flow from the regenerator matrix to the working gas. A new definition of regenerator figure-of-merit is proposed for the intermediate expansion stages based on a stage energy balance, and its evaluation and uses in design are discussed. The analysis of a typical three expansion stage cryocooler is presented.