Process for producing hydrogen-enriched synthesis gas by means of a catalytic gas-to-water displacement reaction carried out on a crude synthesis gas, comprising the following steps: - introducing a gas stream comprising at least one compound of formula in which R is chosen from a linear or branched alkyl radical containing from 1 to 4 carbon atoms, and a linear or branched alkenyl radical containing from 2 to 4 carbon atoms, n is equal to 0, 1 or 2, x is an integer chosen from 0, 1, 2, 3 or 4, R' is chosen from a linear or branched alkyl radical containing from 1 to 4 carbon atoms, a linear or branched alkenyl radical containing from 2 to 4 carbon atoms and, only when n=x=0, a hydrogen atom, in a first reactor comprising a catalyst X 1, said catalyst X 1 comprising at least one metal chosen from groups VIB and VII of the periodic table, - collecting a gas stream containing sulfur from the first reactor, - introducing the crude synthesis gas into a second reactor, - introducing the gas stream containing sulfur into the second reactor where the catalytic gas-to-water displacement reaction takes place and comprising a sulfur resistant displacement catalyst X 2, the gas stream containing sulfur being introduced into the second reactor directly by means of the stream (3.1) and/or after mixing by means of the stream (3.2) with the crude synthesis gas, - collecting an output stream from the second reactor, said output stream comprising a hydrogen-enriched synthesis gas. - introducing a gas stream comprising at least one compound of formula in which R is chosen from a linear or branched alkyl radical containing from 1 to 4 carbon atoms, and a linear or branched alkenyl radical containing from 2 to 4 carbon atoms, n is equal to 0, 1 or 2, x is an integer chosen from 0, 1, 2, 3 or 4, R' is chosen from a linear or branched alkyl radical containing from 1 to 4 carbon atoms, a linear or branched alkenyl radical containing from 2 to 4 carbon atoms and, only when n=x=0, a hydrogen atom, in a first reactor comprising a catalyst X 1, said catalyst X 1 comprising at least one metal chosen from groups VIB and VII of the periodic table, in which R is chosen from a linear or branched alkyl radical containing from 1 to 4 carbon atoms, and a linear or branched alkenyl radical containing from 2 to 4 carbon atoms, n is equal to 0, 1 or 2, x is an integer chosen from 0, 1, 2, 3 or 4, R' is chosen from a linear or branched alkyl radical containing from 1 to 4 carbon atoms, a linear or branched alkenyl radical containing from 2 to 4 carbon atoms and, only when n=x=0, a hydrogen atom, in a first reactor comprising a catalyst X 1, said catalyst X 1 comprising at least one metal chosen from groups VIB and VII of the periodic table, - collecting a gas stream containing sulfur from the first reactor, - introducing the crude synthesis gas into a second reactor, - introducing the gas stream containing sulfur into the second reactor where the catalytic gas-to-water displacement reaction takes place and comprising a sulfur resistant displacement catalyst X 2, the gas stream containing sulfur being introduced into the second reactor directly by means of the stream (3.1) and/or after mixing by means of the stream (3.2) with the crude synthesis gas, - collecting an output stream from the second reactor, said output stream comprising a hydrogen-enriched synthesis gas.