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A complete classification of stable homotopy types of complex and quaternionic stunted projective spaces, denoted by CPnk and QPnk respectively, is obtained. The necessary conditions for such equivalences are found using Ä-theory and various characteristic classes introduced originally by J. F. Adams. As a by-product one finds the /-orders of the Hopf bundles over CP" and QP" respectively. The algebraic part is rather involved. Finally a homotopy theoretical argument yields the constructions ofdoi:10.2307/1997492 fatcat:rotpsbebnfdwliucgwydyljage