The controversy about the position of the matter accumulation that causes our peculiar motion with respect to the cosmic background radiation (CBR) has very recently acquired great interest. So, the very local attractor suggested by Lynden-Bell et al. (1988) and Dressler (1988) begins to be questioned. The histogram done by Melnick and Moles (1987) shows that the dominant structure may be at ~140 h−1 Mpc. Similar results have been obtained by Scaramella et al. (1989). On the other hand, the analysis of the very local candidate in the X-ray band shows that this does not have rich clusters of galaxies (Jahoda and Mushotzky 1989). Moreover, Lahav et al. (1989) have studied a sample of 53 clusters emitting X-rays (E ≈ 2–20 keV, LX ≈ 5 × 1042–7 × 1044h−2 erg s−1); they have observed a great concentration of clusters in the direction of the attractor suggested by Lynden-Bell et al., but at a distance of ~100 h−1–150 h−1 Mpc. The detections of nonlocal structures (further than 300 h−1 Mpc) are very few. However, the study done by Shaver (1987) using catalogs of quasars showed that a superstructure with a radius of ~200 h−1 Mpc and with a density in excess of δ ≈ 1 may exist at a distance of ~800 h−1 Mpc.