Sorption of tracer amounts of 137Cs and 90Sr radionuclides from model solutions of various compositions onto synthetic titanosilicates, framework ivanyukite and layered SL3, both synthesized at the Center for Nanomaterials Science, Kola Scientific Center, Russian Academy of Sciences, was studied. Synthetic ivanyukite and titanosilicate SL3 well compete with Termoxid-25 ferrocyanide sorbent in the ability to take up cesium from neutral NaNO3 solutions and from a simulated solution of bottom residue from a nuclear power plant with RBMK reactors. The maximal sorption of 137Cs onto ivanyukite is observed at pH 6–7. The dependence of the 137Cs distribution coefficient (K d) on ivanyukite on the concentration of sodium and potassium ions in the solution was studied. Potassium ions affect the cesium sorption more strongly than sodium ions do. In the ability to take up 90Sr, synthetic ivanyukite well competes with synthetic zeolite of type A and with the sorbent based on modified manganese dioxide. The dependences of K d of 90Sr on the concentrations of the Na+ and Ca2+ ions in the solution were determined. Calcium ions affect the strontium sorption more strongly than sodium ions do. Ivanyukite and SL3 show promise as sorbents for removing cesium and strontium radionuclides from multicomponent salt solutions.