A method for the demercurisation of flue gases, in which the flue gases to be treated are sent to a solid gas separator, in which a demercurisation reagent is introduced into the flue gas upstream of the solid gas separator, in which a recycled fraction of the solids collected by the solid gas separator is sent to a treatment device for reactivation, before being introduced, via a flow leaving the treatment device, into the flue gases upstream of the solid gas separator, and in which the demercurisation reagent is dosed by carrying out the following operations at each instant: a) a mercury concentration value (Cc) is determined from (i) the mercury concentration in the flue gases upstream of the points where the demercurisation reagent is introduced into the flue gases and the flow leaving the treatment device and/or (ii) the mercury concentration in the flue gases downstream of the solid gas separator, and b) the occurrence of mercury peaks is taken into account so that: - outside a period (P1, P2) which begins substantially at the peak of each mercury peak, the demercurisation reagent is dosed by applying to the mercury concentration value (Cc) a first dosing function (f) which increases with the mercury concentration value (Cc), and - during the said period (P1, P2), the demercurisation reagent is dosed by applying to the mercury concentration value (Cc) a second dosing function (g) which doses the demercurisation reagent at a value greater than that at which the demercurisation reagent is dosed by the first dosing function (f) at the instant in question, the second dosing function decreasing with time until the demercurisation reagent is dosed at a value equal to or less than that at which the demercurisation reagent is dosed by the first dosing function at a time when the said period ends. in which the flue gases to be treated are sent to a solid gas separator, in which a demercurisation reagent is introduced into the flue gas upstream of the solid gas separator, in which a recycled fraction of the solids collected by the solid gas separator is sent to a treatment device for reactivation, before being introduced, via a flow leaving the treatment device, into the flue gases upstream of the solid gas separator, and in which the demercurisation reagent is dosed by carrying out the following operations at each instant: a) a mercury concentration value (Cc) is determined from (i) the mercury concentration in the flue gases upstream of the points where the demercurisation reagent is introduced into the flue gases and the flow leaving the treatment device and/or (ii) the mercury concentration in the flue gases downstream of the solid gas separator, and b) the occurrence of mercury peaks is taken into account so that: - outside a period (P1, P2) which begins substantially at the peak of each mercury peak, the demercurisation reagent is dosed by applying to the mercury concentration value (Cc) a first dosing function (f) which increases with the mercury concentration value (Cc), and - during the said period (P1, P2), the demercurisation reagent is dosed by applying to the mercury concentration value (Cc) a second dosing function (g) which doses the demercurisation reagent at a value greater than that at which the demercurisation reagent is dosed by the first dosing function (f) at the instant in question, the second dosing function decreasing with time until the demercurisation reagent is dosed at a value equal to or less than that at which the demercurisation reagent is dosed by the first dosing function at a time when the said period ends. a) a mercury concentration value (Cc) is determined from (i) the mercury concentration in the flue gases upstream of the points where the demercurisation reagent is introduced into the flue gases and the flow leaving the treatment device and/or (ii) the mercury concentration in the flue gases downstream of the solid gas separator, and b) the occurrence of mercury peaks is taken into account so that: - outside a period (P1, P2) which begins substantially at the peak of each mercury peak, the demercurisation reagent is dosed by applying to the mercury concentration value (Cc) a first dosing function (f) which increases with the mercury concentration value (Cc), and - during the said period (P1, P2), the demercurisation reagent is dosed by applying to the mercury concentration value (Cc) a second dosing function (g) which doses the demercurisation reagent at a value greater than that at which the demercurisation reagent is dosed by the first dosing function (f) at the instant in question, the second dosing function decreasing with time until the demercurisation reagent is dosed at a value equal to or less than that at which the demercurisation reagent is dosed by the first dosing function at a time when the said period ends. - outside a period (P1, P2) which begins substantially at the peak of each mercury peak, the demercurisation reagent is dosed by applying to the mercury concentration value (Cc) a first dosing function (f) which increases with the mercury concentration value (Cc), and - during the said period (P1, P2), the demercurisation reagent is dosed by applying to the mercury concentration value (Cc) a second dosing function (g) which doses the demercurisation reagent at a value greater than that at which the demercurisation reagent is dosed by the first dosing function (f) at the instant in question, the second dosing function decreasing with time until the demercurisation reagent is dosed at a value equal to or less than that at which the demercurisation reagent is dosed by the first dosing function at a time when the said period ends.