Method for observing a state of an electrochemical system including a fuel cell that is formed from at least one electrochemical cell comprising an anode and a cathode separated from each other by a membrane, further including an anodic distribution circuit for distributing hydrogen that is linked to an anodic fluid discharge line provided with a purge valve controlled on the basis of a signal, referred to as the purge signal (Q ao), and a cathodic distribution circuit for distributing oxygen, said method including the following steps: a) measuring, at a measurement time (t k), an electric current of the fuel cell, a voltage of the fuel cell, a pressure, referred to as the anodic pressure (P a), of the anodic distribution circuit, a pressure, referred to as the cathodic pressure (P c), of the cathodic distribution circuit, and a temperature of the fuel cell; b) forming a control vector on the basis of the purge signal (Q ao) and of the measurements of the electric current, of the temperature and of the cathodic pressure (P c); c) forming a measurement vector on the basis of an ohmic resistance value (Rm) of the membrane deduced from the measurements of the electric current and of the voltage, and on the basis of the measurement of the anodic pressure (P a); d) calculating a temporal variation, referred to as a non-corrected temporal variation X ^ ̇ nc, on the basis of a prior estimate (X̂) of the state and of the control vector, based on a predetermined representation (f) of the state of the electrochemical system, the state being formed from state variables that are representative of the amounts of nitrogen n N 2 a and of hydrogen n H 2 a at the anode, and of the amounts of water at the anode n H 2 O a, at the cathode n H 2 O c, and in the membrane ( λ m); e) calculating a corrective term (ε) in sliding mode on the basis of a difference between the measurement vector and an estimate, referred to as a measurement estimate (Ŷ) of the measurement vector obtained on the basis of a prior estimate (X̂) of the state; f) calculating an estimate (X̂) of said state of the electrochemical system for the measurement time (tk), on the basis of the non-corrected temporal variation X ^ ̇ nc and of the corrective term (ε); g) reiterating steps a) to f) while incrementing the measurement time, the prior estimate (X̂) of steps d) and e) then corresponding to the state estimate (X̂) calculated in the preceding iteration. a) measuring, at a measurement time (t k), an electric current of the fuel cell, a voltage of the fuel cell, a pressure, referred to as the anodic pressure (P a), of the anodic distribution circuit, a pressure, referred to as the cathodic pressure (P c), of the cathodic distribution circuit, and a temperature of the fuel cell; b) forming a control vector on the basis of the purge signal (Q ao) and of the measurements of the electric current, of the temperature and of the cathodic pressure (P c); c) forming a measurement vector on the basis of an ohmic resistance value (Rm) of the membrane deduced from the measurements of the electric current and of the voltage, and on the basis of the measurement of the anodic pressure (P a); d) calculating a temporal variation, referred to as a non-corrected temporal variation X ^ ̇ nc, on the basis of a prior estimate (X̂) of the state and of the control vector, based on a predetermined representation (f) of the state of the electrochemical system, the state being formed from state variables that are representative of the amounts of nitrogen n N 2 a and of hydrogen n H 2 a at the anode, and of the amounts of water at the anode n H 2 O a, at the cathode n H 2 O c, and in the membrane ( λ m); e) calculating a corrective term (ε) in sliding mode on the basis of a difference between the measurement vector and an estimate, referred to as a measurement estimate (Ŷ) of the measurement vector obtained on the basis of a prior estimate (X̂) of the state; f) calculating an estimate (X̂) of said state of the electrochemical system for the measurement time (tk), on the basis of the non-corrected temporal variation X ^ ̇ nc and of the corrective term (ε); g) reiterating steps a) to f) while incrementing the measurement time, the prior estimate (X̂) of steps d) and e) then corresponding to the state estimate (X̂) calculated in the preceding iteration.