A method for absorbing acid compounds contained in a gaseous effluent wherein the gaseous effluent is contacted with an absorbent solution, said solution comprising: a) at least one amine, b) water, c) at least one degradation inhibiting compound for limiting the degradation of said amine, said degradation inhibiting compound meeting one of the following general formulas: wherein X is selected from among: ∘ a hydrogen atom, ∘ an alkaline or alkaline-earth element, ∘ a monovalent or multivalent metal, ∘ an ammonium cation NH 4 + or resulting from the protonation of an amine function, ∘ a phosphonium cation, wherein each radical R 1, R 2 and R 3 is independently selected from among: ∘ a hydrogen atom, ∘ a hydrocarbon radical comprising 1 to 12 carbon atoms, ∘ a radical wherein W is selected from among a sulfur atom and an oxygen atom and Y is selected from among: ∘ a hydrogen atom, ∘ a hydrocarbon radical comprising 1 to 12 carbon atoms, ∘ an alkaline or alkaline-earth element, ∘ a monovalent or multivalent metal, ∘ an ammonium cation NH 4 + or resulting from the protonation of an amine function, ∘ a phosphonium cation, and wherein each radical R 4 and R 5 is independently selected from among: ∘ a hydrogen atom, ∘ a hydrocarbon radical comprising 1 to 12 carbon atoms. a) at least one amine, b) water, c) at least one degradation inhibiting compound for limiting the degradation of said amine, said degradation inhibiting compound meeting one of the following general formulas: wherein X is selected from among: ∘ a hydrogen atom, ∘ an alkaline or alkaline-earth element, ∘ a monovalent or multivalent metal, ∘ an ammonium cation NH 4 + or resulting from the protonation of an amine function, ∘ a phosphonium cation, wherein each radical R 1, R 2 and R 3 is independently selected from among: ∘ a hydrogen atom, ∘ a hydrocarbon radical comprising 1 to 12 carbon atoms, ∘ a radical wherein W is selected from among a sulfur atom and an oxygen atom and Y is selected from among: ∘ a hydrogen atom, ∘ a hydrocarbon radical comprising 1 to 12 carbon atoms, ∘ an alkaline or alkaline-earth element, ∘ a monovalent or multivalent metal, ∘ an ammonium cation NH 4 + or resulting from the protonation of an amine function, ∘ a phosphonium cation, and wherein each radical R 4 and R 5 is independently selected from among: ∘ a hydrogen atom, ∘ a hydrocarbon radical comprising 1 to 12 carbon atoms. ∘ a hydrogen atom, ∘ an alkaline or alkaline-earth element, ∘ a monovalent or multivalent metal, ∘ an ammonium cation NH 4 + or resulting from the protonation of an amine function, ∘ a phosphonium cation, ∘ a hydrogen atom, ∘ a hydrocarbon radical comprising 1 to 12 carbon atoms, ∘ a radical wherein W is selected from among a sulfur atom and an oxygen atom and Y is selected from among: ∘ a hydrogen atom, ∘ a hydrocarbon radical comprising 1 to 12 carbon atoms, ∘ an alkaline or alkaline-earth element, ∘ a monovalent or multivalent metal, ∘ an ammonium cation NH 4 + or resulting from the protonation of an amine function, ∘ a phosphonium cation, ∘ a hydrogen atom, ∘ a hydrocarbon radical comprising 1 to 12 carbon atoms, ∘ an alkaline or alkaline-earth element, ∘ a monovalent or multivalent metal, ∘ an ammonium cation NH 4 + or resulting from the protonation of an amine function, ∘ a phosphonium cation, ∘ a hydrogen atom, ∘ a hydrocarbon radical comprising 1 to 12 carbon atoms.