In this paper we propose and test a new method of multitemperature analysis of solar X-ray spectra. The method, which is based on a technique developed by Withbroe (1975), is designed to be used in the interpretation of spectra, to be measured by the X-Ray Polychromator on the Solar Maximum Mission. Various tests of the method on simulated temperature models establish its usefulness, generality, and stability. The possibilities of deriving the relative element abundances are analysed. The results of the present paper extend the possibility of the multitemperature analysis of X-ray spectra as compared with the results of Craig and Brown (1976a, b) and Craig (1977).