The work investigates the corrosion behavior of nickel, rhenium, and their alloys in concentrated nonoxidizing and oxidizing acids. The mechanism of the corrosion dissolution of nickel-rhenium alloys in concentrated hydrochloric and nitric acids is proposed. Based on X-ray studies, the predominant dissolution of nickel from the surface of nickel-rhenium alloys is established. Etching occurs mainly from certain edges, especially along the [111] plane. The introduction of rhenium into nickel in an amount of 5, 10, and 20 wt % has an ambiguous effect on the corrosion rate of the entire alloy and, depending on the ratio of nickel and rhenium in the alloy, the corrosion rate of the alloy in nonoxidizing and oxidizing acids can both decrease and increase. An alloy with 20% rhenium is limiting in concentrated hydrochloric acid from the point of view of achieving the required concentration of rhenium on the surface and reducing the rate of dissolution of the alloys. In concentrated nitric acid and aqua regia, an increase in the rhenium content in the alloy above 10% is impractical, since the corrosion rate increases significantly. An increased rate of dissolution of alloys in nitric acid compared to hydrochloric acid is established.