Experiments with Xi(-) atoms are proposed in order to study the nuclear interaction of Xi hyperons. The production of Xi(-) in the (K-,K+) reaction, the Xi(-) stopping in matter, and its atomic cascade are incorporated within a realistic evaluation of the results expected for Xi(-) x-ray spectra across the periodic table, using an assumed Xi-nucleus optical potential V-opt. Several optimal targets far measuring the strong-interaction shift and width of the x-ray transition to the "last" atomic level observed are singled out: F, Cl, I, and Pb. The sensitivity of these observables to the parameters of V-opt is considered. The relevance of such experiments is discussed in the context of strangeness -2. nuclear physics and multistrange nuclear matter. Finally, with particular reference to searches for the H dibaryon, the properties of Xi(-)d atoms are also discussed. The role of Stark mixing and its effect on S and P state capture of Xi(-) by the deuteron together with estimates of the resulting probability for producing the H dibaryon are considered in detail. [S0556-2813(99)02601-1].