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We have solved the set of equations for advection-dominated accretion flows (ADAFs) around black holes, and found a new class of global solutions with standing radial shocks. Such α-X-type shocks may exist in flows when 0 ≤ α < 0.05. An example solution is given explicitly, for which α = 0.01 and γ = 1.5. The shock position is Rsh = 8.68Rg, which is between the inner sonic point Rs1 = 3.88Rg and the outer sonic point Rs2 = 85.92Rg.