- A method for evaluating ageing of a three-way catalyst for an assembly comprising: a) a spark ignition internal combustion engine ; b) an exhaust after-treatment system comprising a three-way catalyst ; c) a lambda sensor (LSF) arranged downstream of said catalyst , considering a flow direction of exhaust gases in said catalyst ; said lambda sensor (LSF) generating an actual output signal (U); and d) an injection device supplying fuel to said engine ; the method comprising the step of controlling said injection device according to a set-point (λset), indicative of a desired air/fuel ratio during combustion of a mixture of fuel and air in said engine ; wherein the method comprises the steps of: - setting a wobbling pattern for said set-point (λset) so as to operate said engine with alternating lean combustion phases and rich combustion phases; - calculating a first value of a parameter that is indicative of a signal amplitude, said first value being calculated in relation to said actual output signal (U); - comparing said first value with a reference so as to evaluate a possible ageing of the three-way catalyst; characterized by comprising the steps of: - simulating said catalyst by a catalyst model; - generating, in said catalyst model, data (D3) indicative of an estimated composition of exhaust gases exiting from said catalyst ; - simulating said lambda sensor (LSF) by a sensor model; - generating an estimated output signal (Umod) in said sensor model, on the basis of said data (D3); - calculating a second value of said parameter, said second value being calculated in relation to said estimated output signal (Umod); - determining said reference as a function of said second value. a) a spark ignition internal combustion engine ; b) an exhaust after-treatment system comprising a three-way catalyst ; c) a lambda sensor (LSF) arranged downstream of said catalyst , considering a flow direction of exhaust gases in said catalyst ; said lambda sensor (LSF) generating an actual output signal (U); and d) an injection device supplying fuel to said engine ; the method comprising the step of controlling said injection device according to a set-point (λset), indicative of a desired air/fuel ratio during combustion of a mixture of fuel and air in said engine ; - setting a wobbling pattern for said set-point (λset) so as to operate said engine with alternating lean combustion phases and rich combustion phases; - calculating a first value of a parameter that is indicative of a signal amplitude, said first value being calculated in relation to said actual output signal (U); - comparing said first value with a reference so as to evaluate a possible ageing of the three-way catalyst; - simulating said catalyst by a catalyst model; - generating, in said catalyst model, data (D3) indicative of an estimated composition of exhaust gases exiting from said catalyst ; - simulating said lambda sensor (LSF) by a sensor model; - generating an estimated output signal (Umod) in said sensor model, on the basis of said data (D3); - calculating a second value of said parameter, said second value being calculated in relation to said estimated output signal (Umod); - determining said reference as a function of said second value. <EOS>