The transmission high electron energy diffraction (THEED) technique was employed for studying the structure of the equimolar Ar-Kr alloy, in which the thermodynamics predicts the maximum feasibility of phase separation. Deposition of preliminarily cooled gas mixtures was performed onto substrates cooled to 6 or 20 K. All diffraction patterns contained several sets of reflections against an appreciable background. Analysis of the data obtained during a warm-up from 6 to 33 K (at which the major part of argon was removed due to sublimation) as well as of the diffraction pattern from the "sandwich" (two successively deposited film of pure Ar and Kr) provided reliable arguments for the following conclusions. Actually, we have documented for the first time a phase separation of an Ar-Kr mixture, manifestations of which turned out to be oddly asymmetric as far as the behavior of the components involved is concerned. Upon deposition both onto 6 or 20 K the emerging sample contained two crystal phases of virtually pure argon with a small admixture of krypton. One of the Ar phases (fcc) did not cause a surprise, whereas the other was hcp with the a/c ratio close to the ideal value. The krypton component separated as a fine-grained glass-like state, possibly, with a low admixture of argon.