Molten fluorides of alkali metals are considered a technological medium for molten salt reactors (MSRs). However, these media are known to be extremely corrosive. The successful implementation of high-temperature technological devices using molten alkali metal fluorides requires the selection of such structural materials that have high corrosion resistance in melts with compositional characteristic of MSRs. In this research, the corrosion behavior of 12Cr18Ni10Ti steel, the alloy Ni60Cr20Mo15, and the alloy Monel 404 (Ni50Cu50) was investigated in the LiF–NaF–KF eutectic melt, containing additions of CeF₃ and NdF₃ from 0 to 5 wt.% as imitator fluorides of actinides in an inert argon atmosphere at 550 °C for 100 h. Gravimetry, energy-dispersive X-ray (EDX) microanalysis of surfaces and cross-section of samples, and ICP-MS were used to establish the corrosion behavior of the investigated alloys. Corrosion resistance of the studied materials was found to decrease in a row from Monel 404 > Hastelloy C2000 > 12Cr18Ni10Ti. The addition of cerium fluoride into the melt resulted in the additional etching of the alloy surface. The addition of neodymium fluoride resulted in the formation of the point/inter-crystalline corrosion damages in the sample bulk. The samples of steel 12Cr18Ni10Ti were subjected to local cracking corrosion. The austenitic nickel-based alloys suffered specific local corrosion with formation of subsurface voids. Excellent corrosion resistance of the Monel alloy under the test conditions was found.