Let G be a compact Lie group and P a set of primes. Consider the category of G-simply connected, G-based G-spaces and equivariant maps. Equivariant localization at P has been defined and studied by J. P. May, J. McClure and G. Triantafillou [Bull. Lond. Math. Soc. 14, 223- 230 (1982; Zbl 0492.57012)]. Here the author proves that for G-CW-spaces (satisfying certain conditions) the localization can be obtained via a telescoping procedure. He also investigates uniqueness and functoriality of his more general constructions (in the homotopy category).